SlideShare ist ein Scribd-Unternehmen logo
1 von 12
Downloaden Sie, um offline zu lesen
Calculation of Arithmetic Mean
Arithmetic Mean
• Arithmetic mean is one of the methods of calculating central
tendency.
• It is an average.
• It is calculated to reach a single value which represents the entire
data.
• Calculating an Average
• For example (1, 2, 2, 2, 3, 9). The arithmetic mean is
1 + 2 + 2 + 2 + 3 + 9
6
= 19/6 = 3.17
Arithmetic means are used in situations such as working out cricket
averages.
• Arithmetic means are used in calculating average incomes.
Different Series and different methods
• Individual Series
» Direct Method
» Shortcut Method
• Discrete Series
» Direct Method
» Shortcut Method
• Continuous Series
» Direct Method
» Shortcut Method
» Step Deviation Method
Individual Series - Direct Method
Student A B C D E F G H I J
Marks 2 7 10 8 6 3 5 4 5 0
The Problem – Calculate the arithmetic mean for the data given below
1. Write the sum in rows and column format.Student X
A 2
B 7
C 10
D 8
E 6
F 3
G 5
H 4
I 5
J 0
2. Formula to find the arithmetic mean=
= 2+7+10+8+6+3+5+4+5+0
10
= 50
10
= 5
Ans : The arithmetic mean is 5
50
∑x Nis the number of
observations
N is the number of
observations in our
e.g. there are 10
students so N =10
Individual Series: Shortcut Method
Student A B C D E F G H I J
Marks 2 7 10 8 6 3 5 4 5 0
2. Assume a Mean (A) = 2
1. Draw 2 columns ;
a. Under X write the marks.
b. dx = X-A
3. Formula to find the arithmetic mean =
= 2 + 0+5+8+6+4+1+3+2+3(-2)
10
= 2 + 32-2
10
= 2+3 = 5
Ans : The arithmetic mean is 5
=2 + 30
10
X
2
7
10
8
6
3
5
4
5
0
A = 2
dx = X - A
2 -2 = 0
7- 2 = 5
10 - 2 = 8
8 - 2 = 6
6 - 2 = 4
3 -2 = 1
5 -2 = 3
4 -2 = 2
5 - 2 = 3
0 - 2= -2
30
= A + ∑dx / N
Discrete Series- Direct method
Marks Received by students 5 2 3 4
Frequency 4 6 8 6
Step 1. Column ‘x’ and put all the data
of marks received by students in this
column.
Step 2. Column ‘’f and put all the data
of frequency under this.
Step 3. Third column ‘fx’ ; fx = f x X
i.e multiply data in col. f with data in
col. X.
Step 4. Find ∑fx add all the data in
column ‘ fx’ = 20+ 12 +24 +24 = 80
Step 5. Find ∑f Add all data in column ‘f’
= 4+6+8+6 = 24
Step 6 .Formula to find mean =
(∑fx)
(∑f)
= 80/24 = 3.33 ; ANS = 3.33
x
Marks Received by students
5
2
3
4
f
Frequency
4
6
8
6
24
fx
4 x 5 = 20
6 x 2 = 12
8 x 3 = 24
6 x 4 = 24
80
Discrete Series- Shortcut method
Marks Received by students 5 2 3 4
Frequency 4 6 8 6
Step 1. Make a column ‘x’ and put all the data
of marks received by students in this column.
Step 2. Column ‘’f and put all the data of
frequency under this.
Step 3. Column Assume a no. A
in our e.g. we have assumed A = 2
‘dx’ ; dx = x -A
Step 4. Find ∑fdx Multiply data in column
‘f’ with data in column ‘dx’.
∑fdx = sum of the column fdx = 32
Step 5. Find ∑f Add all data in column ‘f’
= 4+6+8+6 = 24
Step 6 . Formula = A + (∑fdx)/(∑f)
= 2 + 32/24 = 3.33 ; ANS = 3.33
x
Marks Received by students
5
2
3
4
f
Frequency
4
6
8
6
A = 2
dx = x - A
5 - 2= 3
2 - 2= 0
3 - 2= 1
4 - 2= 2
fdx
4 x 3 = 12
6 x 0 = 0
8 x 1 = 8
6 x 2 = 12
24 32
Continuous Series - Direct Method
The following table shows wages of workers. Calculate the arithmetic mean.
Wages 10 - 20 20-30 30 - 40 40 - 50 50 - 60
No. of Workers 8 9 12 11 6
The wages are given in a group series
e.g. how many workers get wages between 10 to 20 Ans. 8.
How many workers get wages between 20 and 30 Ans. 9.
Here ‘X’ is the wages, but we cannot identify one number for ‘X’.
So we need to find the ‘Mid Value’ of each group.
e.g. To find the Mid value of the first group ‘10 – 20’
Formula to find the Mid Value
L1 + L2/ 2
L1 = the first number in the group in our example it is ‘10’
L2 = the second number in the group, in our example it is ‘20 ‘
Divide by 2, because we need to divide into two halves
so we know which number is in the middle.
So the mid value (M.V) for the first group ‘10 – 20’ =
10 + 20 / 2 = 30 /2 = 15
Arrange the numbers in the following manner
Add a column “MV”(Mid Value) which will be your new ‘X’, and find the Mid Value
X
MV (Mid Value)
10+20/2 = 15
20+30/2 = 25
30+40/2= 35
40+50/2 = 45
50+60/2 = 55
Formula = ∑fx/ ∑fWages
f
No. of Workers
10 - 20 8
20-30 9
30 - 40 12
40 - 50 11
50 - 60 6
Add another column ‘fx’ i.e multiple value in column ‘f’ and the value in column ‘X’.
fx
8 x 15 = 120
9 x 25 = 225
12 x 35 = 420
11 x 45 = 495
6 x 55 = 330
Find ∑f i.e (find the total of column ‘f’) Find ∑fx i.e (find the total of column ‘fx’)
∑f = 46 ∑fx 1590
= 1590
46
Answer = 34.56
Continuous Series - Direct Method.. Cont.….
Continuous Series – Shortcut Method
Wages
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
f
No.of Workers
8
9
12
11
6
46
x
Mid Value
10 + 20/2 = 15
20 + 30/2= 25
30 + 40 /2 = 35
40 + 50/2 = 45
50 + 60/2 = 55
Assume A = 15
dx = x - A
dxf
15 - 15 = 0
25 - 15= 10
35 - 15= 20
45 - 15= 30
55 - 15= 40
1.Draw the 3 columns similar to the direct method i.e Wages, f (no.of workers and x-Midvalue)
2. Next assume a no. A (preferably from column’x’). In our eg we have assumed A = 15.
3. Find dx, dx = x – A.
4. Find fdx ; Multiply the answer in dx column with the 2nd column ‘f’.
5. Formula to find the arithmetic mean = A + ∑fdx
∑f
= A + ∑fdx
∑f
= 15 + 900
46
Answer = 34.56
fdx
0 x 8 = 0
10 x 9 = 90
20 x 12 = 240
30 x 11 = 330
40 x 6 = 240
900
Continuous Series – Step deviation Method
1.Draw the columns similar to the shortcut method i.e Wages, f, x and dx
2. Next assume a no. C. In our eg we have assumed c = 10.
3. Find dx’, dx’= dx /c.
4. Find fdx’ ; Multiply the answer in dx’ column with the 2nd column ‘f’.
5. Formula to find the arithmethic mean = A + ∑fdx’ x c
∑f
= A + ∑fdx’ x c
∑f
Answer = 34.56
Wages
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
f
No.of Workers
8
9
12
11
6
46
x
Mid Value
10 + 20/2 = 15
20 + 30/2= 25
30 + 40 /2 = 35
40 + 50/2 = 45
50 + 60/2 = 55
Assume A = 15
dx = x - A
dxf
15 - 15 = 0
25 - 15= 10
35 - 15= 20
45 - 15= 30
55 - 15= 40
Assume C= 10
dx' = dx/c
0/10 = 0
10/10= 1
20/10= 2
30/10= 3
40/10= 4
Individual Series
Direct Method :
Shortcut Method :
Discrete Series
Direct Method : = ∑fx
∑f
Shortcut Method : = A + ∑fdx
∑f
Continuous Series
Direct Method
Shortcut Method
Step Deviation
X
X dx
X f dx fdx
X f fx
X f x(M.V) fx
No. of Boxes
x f x (M.V) dx fdx
x f x (M.V) dx dx' fdx'

Weitere ähnliche Inhalte

Was ist angesagt?

Coefficient of variation
Coefficient of variationCoefficient of variation
Coefficient of variationNadeem Uddin
 
Mean, median, mode, & range ppt
Mean, median, mode, & range pptMean, median, mode, & range ppt
Mean, median, mode, & range pptmashal2013
 
Measures of dispersion
Measures of dispersionMeasures of dispersion
Measures of dispersionSachin Shekde
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendencyAlex Chris
 
Measure OF Central Tendency
Measure OF Central TendencyMeasure OF Central Tendency
Measure OF Central TendencyIqrabutt038
 
Standard Deviation and Variance
Standard Deviation and VarianceStandard Deviation and Variance
Standard Deviation and VarianceJufil Hombria
 
Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Jan Nah
 
Introduction to business statistics
Introduction to business statisticsIntroduction to business statistics
Introduction to business statisticsAakash Kulkarni
 
frequency distribution
 frequency distribution frequency distribution
frequency distributionUnsa Shakir
 
Ogive presentation
Ogive presentationOgive presentation
Ogive presentationSajidBepari
 
Measures of central tendency ppt
Measures of central tendency pptMeasures of central tendency ppt
Measures of central tendency pptNighatKanwal
 
Measures of Variation or Dispersion
Measures of Variation or Dispersion Measures of Variation or Dispersion
Measures of Variation or Dispersion Dr Athar Khan
 

Was ist angesagt? (20)

mean median mode
 mean median mode mean median mode
mean median mode
 
MEAN.pptx
MEAN.pptxMEAN.pptx
MEAN.pptx
 
Coefficient of variation
Coefficient of variationCoefficient of variation
Coefficient of variation
 
Mean, median, mode, & range ppt
Mean, median, mode, & range pptMean, median, mode, & range ppt
Mean, median, mode, & range ppt
 
Arithematic mean
Arithematic meanArithematic mean
Arithematic mean
 
Median
MedianMedian
Median
 
Measures of dispersion
Measures of dispersionMeasures of dispersion
Measures of dispersion
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 
Measure OF Central Tendency
Measure OF Central TendencyMeasure OF Central Tendency
Measure OF Central Tendency
 
MEAN DEVIATION
MEAN DEVIATIONMEAN DEVIATION
MEAN DEVIATION
 
Standard Deviation and Variance
Standard Deviation and VarianceStandard Deviation and Variance
Standard Deviation and Variance
 
Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency
 
Index Number
Index NumberIndex Number
Index Number
 
Introduction to business statistics
Introduction to business statisticsIntroduction to business statistics
Introduction to business statistics
 
frequency distribution
 frequency distribution frequency distribution
frequency distribution
 
To find mode ppt
To find mode  pptTo find mode  ppt
To find mode ppt
 
Ogive presentation
Ogive presentationOgive presentation
Ogive presentation
 
Rank correlation
Rank correlationRank correlation
Rank correlation
 
Measures of central tendency ppt
Measures of central tendency pptMeasures of central tendency ppt
Measures of central tendency ppt
 
Measures of Variation or Dispersion
Measures of Variation or Dispersion Measures of Variation or Dispersion
Measures of Variation or Dispersion
 

Andere mochten auch

Partial Differential Equations, 3 simple examples
Partial Differential Equations, 3 simple examplesPartial Differential Equations, 3 simple examples
Partial Differential Equations, 3 simple examplesEnrique Valderrama
 
Malimu variance and standard deviation
Malimu variance and standard deviationMalimu variance and standard deviation
Malimu variance and standard deviationMiharbi Ignasm
 
ARITHMETIC MEAN AND SERIES
ARITHMETIC MEAN AND SERIESARITHMETIC MEAN AND SERIES
ARITHMETIC MEAN AND SERIESDarwin Santos
 
Propteties of Standard Deviation
Propteties of Standard DeviationPropteties of Standard Deviation
Propteties of Standard DeviationSahil Jindal
 
First order non-linear partial differential equation & its applications
First order non-linear partial differential equation & its applicationsFirst order non-linear partial differential equation & its applications
First order non-linear partial differential equation & its applicationsJayanshu Gundaniya
 
2.3 Histogram/Frequency Polygon/Ogives
2.3 Histogram/Frequency Polygon/Ogives2.3 Histogram/Frequency Polygon/Ogives
2.3 Histogram/Frequency Polygon/Ogivesmlong24
 
Spearman Rank Correlation Presentation
Spearman Rank Correlation PresentationSpearman Rank Correlation Presentation
Spearman Rank Correlation Presentationcae_021
 
Correlation analysis ppt
Correlation analysis pptCorrelation analysis ppt
Correlation analysis pptAnil Mishra
 
Partial differential equations
Partial differential equationsPartial differential equations
Partial differential equationsaman1894
 
Standard deviation
Standard deviationStandard deviation
Standard deviationKen Plummer
 
Standard deviation (3)
Standard deviation (3)Standard deviation (3)
Standard deviation (3)Sonali Prasad
 
Correlation and regression
Correlation and regressionCorrelation and regression
Correlation and regressionKhalid Aziz
 
Skewness & Kurtosis
Skewness & KurtosisSkewness & Kurtosis
Skewness & KurtosisNavin Bafna
 

Andere mochten auch (20)

Partial Differential Equations, 3 simple examples
Partial Differential Equations, 3 simple examplesPartial Differential Equations, 3 simple examples
Partial Differential Equations, 3 simple examples
 
Skewness
SkewnessSkewness
Skewness
 
Malimu variance and standard deviation
Malimu variance and standard deviationMalimu variance and standard deviation
Malimu variance and standard deviation
 
ARITHMETIC MEAN AND SERIES
ARITHMETIC MEAN AND SERIESARITHMETIC MEAN AND SERIES
ARITHMETIC MEAN AND SERIES
 
Propteties of Standard Deviation
Propteties of Standard DeviationPropteties of Standard Deviation
Propteties of Standard Deviation
 
First order non-linear partial differential equation & its applications
First order non-linear partial differential equation & its applicationsFirst order non-linear partial differential equation & its applications
First order non-linear partial differential equation & its applications
 
2.3 Histogram/Frequency Polygon/Ogives
2.3 Histogram/Frequency Polygon/Ogives2.3 Histogram/Frequency Polygon/Ogives
2.3 Histogram/Frequency Polygon/Ogives
 
Spearman Rank
Spearman RankSpearman Rank
Spearman Rank
 
Spearman Rank Correlation Presentation
Spearman Rank Correlation PresentationSpearman Rank Correlation Presentation
Spearman Rank Correlation Presentation
 
Correlation analysis ppt
Correlation analysis pptCorrelation analysis ppt
Correlation analysis ppt
 
Partial differential equations
Partial differential equationsPartial differential equations
Partial differential equations
 
Standard deviation
Standard deviationStandard deviation
Standard deviation
 
Skewness
SkewnessSkewness
Skewness
 
Standard deviation (3)
Standard deviation (3)Standard deviation (3)
Standard deviation (3)
 
Correlation and Simple Regression
Correlation  and Simple RegressionCorrelation  and Simple Regression
Correlation and Simple Regression
 
Pearson Correlation
Pearson CorrelationPearson Correlation
Pearson Correlation
 
Correlation and regression
Correlation and regressionCorrelation and regression
Correlation and regression
 
Correlation ppt...
Correlation ppt...Correlation ppt...
Correlation ppt...
 
Skewness
SkewnessSkewness
Skewness
 
Skewness & Kurtosis
Skewness & KurtosisSkewness & Kurtosis
Skewness & Kurtosis
 

Ähnlich wie Calculation of arithmetic mean

MEAN, MEDIAN AND MODE examples.pptx
MEAN, MEDIAN AND MODE examples.pptxMEAN, MEDIAN AND MODE examples.pptx
MEAN, MEDIAN AND MODE examples.pptxNadimK2
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendencyRaj Teotia
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendencyManu Antony
 
Measures of central tendency - STATISTICS
Measures of central tendency - STATISTICSMeasures of central tendency - STATISTICS
Measures of central tendency - STATISTICSindianeducation
 
Quantitative techniques for MBA (QDM)
Quantitative techniques for MBA (QDM)Quantitative techniques for MBA (QDM)
Quantitative techniques for MBA (QDM)npazare
 
Educational statistics
Educational statisticsEducational statistics
Educational statisticsNishat Anjum
 
Mean (Girja Pd. Patel)
Mean (Girja Pd. Patel)Mean (Girja Pd. Patel)
Mean (Girja Pd. Patel)GirjaPrasad
 
Analysis and interpretation of Assessment.pptx
Analysis and interpretation of Assessment.pptxAnalysis and interpretation of Assessment.pptx
Analysis and interpretation of Assessment.pptxAeonneFlux
 
CENTRAL TENDENCY AND MEAN AND TYPES IN STATISTICS
CENTRAL TENDENCY AND MEAN AND TYPES  IN STATISTICSCENTRAL TENDENCY AND MEAN AND TYPES  IN STATISTICS
CENTRAL TENDENCY AND MEAN AND TYPES IN STATISTICSBALUPRAKASHVITHANALA
 
Central tendency
Central tendencyCentral tendency
Central tendencyAnil Kr Jha
 
Biostatistics Measures of central tendency
Biostatistics Measures of central tendency Biostatistics Measures of central tendency
Biostatistics Measures of central tendency HARINATHA REDDY ASWARTHA
 
Module 4 quadratic functions
Module 4 quadratic functionsModule 4 quadratic functions
Module 4 quadratic functionsdionesioable
 
Statistical Analysis using Central Tendencies
Statistical Analysis using Central TendenciesStatistical Analysis using Central Tendencies
Statistical Analysis using Central TendenciesCelia Santhosh
 
Grouped Data Calculation.pdf
Grouped Data Calculation.pdfGrouped Data Calculation.pdf
Grouped Data Calculation.pdfshamie8
 
Grouped Data Calculation.pdf
Grouped Data Calculation.pdfGrouped Data Calculation.pdf
Grouped Data Calculation.pdfBJYXSZD2
 

Ähnlich wie Calculation of arithmetic mean (20)

MEAN, MEDIAN AND MODE examples.pptx
MEAN, MEDIAN AND MODE examples.pptxMEAN, MEDIAN AND MODE examples.pptx
MEAN, MEDIAN AND MODE examples.pptx
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 
S3 pn
S3 pnS3 pn
S3 pn
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 
Measures of central tendency - STATISTICS
Measures of central tendency - STATISTICSMeasures of central tendency - STATISTICS
Measures of central tendency - STATISTICS
 
Quantitative techniques for MBA (QDM)
Quantitative techniques for MBA (QDM)Quantitative techniques for MBA (QDM)
Quantitative techniques for MBA (QDM)
 
Statistics
StatisticsStatistics
Statistics
 
Educational statistics
Educational statisticsEducational statistics
Educational statistics
 
Mean (Girja Pd. Patel)
Mean (Girja Pd. Patel)Mean (Girja Pd. Patel)
Mean (Girja Pd. Patel)
 
Analysis of data
Analysis of dataAnalysis of data
Analysis of data
 
Analysis and interpretation of Assessment.pptx
Analysis and interpretation of Assessment.pptxAnalysis and interpretation of Assessment.pptx
Analysis and interpretation of Assessment.pptx
 
measures-of-central-tendency.pdf
measures-of-central-tendency.pdfmeasures-of-central-tendency.pdf
measures-of-central-tendency.pdf
 
Airthmetic mean
Airthmetic meanAirthmetic mean
Airthmetic mean
 
CENTRAL TENDENCY AND MEAN AND TYPES IN STATISTICS
CENTRAL TENDENCY AND MEAN AND TYPES  IN STATISTICSCENTRAL TENDENCY AND MEAN AND TYPES  IN STATISTICS
CENTRAL TENDENCY AND MEAN AND TYPES IN STATISTICS
 
Central tendency
Central tendencyCentral tendency
Central tendency
 
Biostatistics Measures of central tendency
Biostatistics Measures of central tendency Biostatistics Measures of central tendency
Biostatistics Measures of central tendency
 
Module 4 quadratic functions
Module 4 quadratic functionsModule 4 quadratic functions
Module 4 quadratic functions
 
Statistical Analysis using Central Tendencies
Statistical Analysis using Central TendenciesStatistical Analysis using Central Tendencies
Statistical Analysis using Central Tendencies
 
Grouped Data Calculation.pdf
Grouped Data Calculation.pdfGrouped Data Calculation.pdf
Grouped Data Calculation.pdf
 
Grouped Data Calculation.pdf
Grouped Data Calculation.pdfGrouped Data Calculation.pdf
Grouped Data Calculation.pdf
 

Mehr von Sajina Nair

nios std x business studies Ch 8 postal and courier services
nios std x business studies Ch 8 postal and courier servicesnios std x business studies Ch 8 postal and courier services
nios std x business studies Ch 8 postal and courier servicesSajina Nair
 
nios std x Business studies Ch 7 communication services
nios std  x Business studies Ch 7 communication servicesnios std  x Business studies Ch 7 communication services
nios std x Business studies Ch 7 communication servicesSajina Nair
 
nios std X business studies Ch 6 Warehousing
nios std X business studies Ch 6 Warehousingnios std X business studies Ch 6 Warehousing
nios std X business studies Ch 6 WarehousingSajina Nair
 
nios std x social science Ch 12 agriculture
nios std x social science Ch 12 agriculturenios std x social science Ch 12 agriculture
nios std x social science Ch 12 agricultureSajina Nair
 
nios Std X Social Science Ch 11biodiversity
nios Std X Social Science Ch 11biodiversitynios Std X Social Science Ch 11biodiversity
nios Std X Social Science Ch 11biodiversitySajina Nair
 
NIOS STD X Economics Ch 20 sectoral aspets
NIOS STD X  Economics Ch 20 sectoral aspetsNIOS STD X  Economics Ch 20 sectoral aspets
NIOS STD X Economics Ch 20 sectoral aspetsSajina Nair
 
NIOS STD X 10th Business Studies Ch 5 transport services
NIOS STD X 10th Business Studies Ch 5 transport servicesNIOS STD X 10th Business Studies Ch 5 transport services
NIOS STD X 10th Business Studies Ch 5 transport servicesSajina Nair
 
NIOS Std X, 10th Business Studies Ch 4 cooperative society
NIOS Std X, 10th Business Studies Ch 4 cooperative societyNIOS Std X, 10th Business Studies Ch 4 cooperative society
NIOS Std X, 10th Business Studies Ch 4 cooperative societySajina Nair
 
NIOS Business Studies Std X Ch 3 Sole proprietorship
NIOS Business Studies Std X Ch 3 Sole proprietorshipNIOS Business Studies Std X Ch 3 Sole proprietorship
NIOS Business Studies Std X Ch 3 Sole proprietorshipSajina Nair
 
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...Sajina Nair
 
Ch 8 cost and revenue
Ch 8 cost and revenueCh 8 cost and revenue
Ch 8 cost and revenueSajina Nair
 
Nios Std X, 10th , Social Science, Ch 8 indian national movement
Nios Std X, 10th , Social Science, Ch 8 indian national movementNios Std X, 10th , Social Science, Ch 8 indian national movement
Nios Std X, 10th , Social Science, Ch 8 indian national movementSajina Nair
 
Ch 5 impact of british rule on india
Ch 5 impact of british rule on indiaCh 5 impact of british rule on india
Ch 5 impact of british rule on indiaSajina Nair
 
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groups
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groupsNIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groups
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groupsSajina Nair
 
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state level
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state levelNIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state level
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state levelSajina Nair
 
Ch 22 peoples participation
Ch 22 peoples participationCh 22 peoples participation
Ch 22 peoples participationSajina Nair
 
NIOS Std X, Social Science Ch 18 local government and field administration
NIOS Std X, Social Science Ch 18 local government and field administrationNIOS Std X, Social Science Ch 18 local government and field administration
NIOS Std X, Social Science Ch 18 local government and field administrationSajina Nair
 

Mehr von Sajina Nair (20)

nios std x business studies Ch 8 postal and courier services
nios std x business studies Ch 8 postal and courier servicesnios std x business studies Ch 8 postal and courier services
nios std x business studies Ch 8 postal and courier services
 
nios std x Business studies Ch 7 communication services
nios std  x Business studies Ch 7 communication servicesnios std  x Business studies Ch 7 communication services
nios std x Business studies Ch 7 communication services
 
nios std X business studies Ch 6 Warehousing
nios std X business studies Ch 6 Warehousingnios std X business studies Ch 6 Warehousing
nios std X business studies Ch 6 Warehousing
 
nios std x social science Ch 12 agriculture
nios std x social science Ch 12 agriculturenios std x social science Ch 12 agriculture
nios std x social science Ch 12 agriculture
 
nios Std X Social Science Ch 11biodiversity
nios Std X Social Science Ch 11biodiversitynios Std X Social Science Ch 11biodiversity
nios Std X Social Science Ch 11biodiversity
 
NIOS STD X Economics Ch 20 sectoral aspets
NIOS STD X  Economics Ch 20 sectoral aspetsNIOS STD X  Economics Ch 20 sectoral aspets
NIOS STD X Economics Ch 20 sectoral aspets
 
NIOS STD X 10th Business Studies Ch 5 transport services
NIOS STD X 10th Business Studies Ch 5 transport servicesNIOS STD X 10th Business Studies Ch 5 transport services
NIOS STD X 10th Business Studies Ch 5 transport services
 
NIOS Std X, 10th Business Studies Ch 4 cooperative society
NIOS Std X, 10th Business Studies Ch 4 cooperative societyNIOS Std X, 10th Business Studies Ch 4 cooperative society
NIOS Std X, 10th Business Studies Ch 4 cooperative society
 
NIOS Business Studies Std X Ch 3 Sole proprietorship
NIOS Business Studies Std X Ch 3 Sole proprietorshipNIOS Business Studies Std X Ch 3 Sole proprietorship
NIOS Business Studies Std X Ch 3 Sole proprietorship
 
Mod 6 ch 17 18
Mod 6 ch 17 18Mod 6 ch 17 18
Mod 6 ch 17 18
 
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...
NIOS STD X Economics Chapter 17 & 18 Collection, Presentation and analysis of...
 
Ch 9 demand
Ch 9 demandCh 9 demand
Ch 9 demand
 
Ch 7 production
Ch 7 productionCh 7 production
Ch 7 production
 
Ch 8 cost and revenue
Ch 8 cost and revenueCh 8 cost and revenue
Ch 8 cost and revenue
 
Nios Std X, 10th , Social Science, Ch 8 indian national movement
Nios Std X, 10th , Social Science, Ch 8 indian national movementNios Std X, 10th , Social Science, Ch 8 indian national movement
Nios Std X, 10th , Social Science, Ch 8 indian national movement
 
Ch 5 impact of british rule on india
Ch 5 impact of british rule on indiaCh 5 impact of british rule on india
Ch 5 impact of british rule on india
 
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groups
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groupsNIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groups
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 21 political parties and pressure groups
 
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state level
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state levelNIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state level
NIOS STD X 10TH, SOCIAL SCIENCE, Ch 19 & ch 20 governance at the state level
 
Ch 22 peoples participation
Ch 22 peoples participationCh 22 peoples participation
Ch 22 peoples participation
 
NIOS Std X, Social Science Ch 18 local government and field administration
NIOS Std X, Social Science Ch 18 local government and field administrationNIOS Std X, Social Science Ch 18 local government and field administration
NIOS Std X, Social Science Ch 18 local government and field administration
 

Kürzlich hochgeladen

HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfMohonDas
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...CaraSkikne1
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17Celine George
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
Philosophy of Education and Educational Philosophy
Philosophy of Education  and Educational PhilosophyPhilosophy of Education  and Educational Philosophy
Philosophy of Education and Educational PhilosophyShuvankar Madhu
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptxraviapr7
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxiammrhaywood
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICESayali Powar
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesCeline George
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17Celine George
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphNetziValdelomar1
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxKatherine Villaluna
 
General views of Histopathology and step
General views of Histopathology and stepGeneral views of Histopathology and step
General views of Histopathology and stepobaje godwin sunday
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?TechSoup
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 

Kürzlich hochgeladen (20)

HED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdfHED Office Sohayok Exam Question Solution 2023.pdf
HED Office Sohayok Exam Question Solution 2023.pdf
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
Finals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quizFinals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quiz
 
Philosophy of Education and Educational Philosophy
Philosophy of Education  and Educational PhilosophyPhilosophy of Education  and Educational Philosophy
Philosophy of Education and Educational Philosophy
 
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptxClinical Pharmacy  Introduction to Clinical Pharmacy, Concept of clinical pptx
Clinical Pharmacy Introduction to Clinical Pharmacy, Concept of clinical pptx
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdfPersonal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICE
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 Sales
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a Paragraph
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptx
 
General views of Histopathology and step
General views of Histopathology and stepGeneral views of Histopathology and step
General views of Histopathology and step
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 

Calculation of arithmetic mean

  • 2. Arithmetic Mean • Arithmetic mean is one of the methods of calculating central tendency. • It is an average. • It is calculated to reach a single value which represents the entire data. • Calculating an Average • For example (1, 2, 2, 2, 3, 9). The arithmetic mean is 1 + 2 + 2 + 2 + 3 + 9 6 = 19/6 = 3.17 Arithmetic means are used in situations such as working out cricket averages. • Arithmetic means are used in calculating average incomes.
  • 3. Different Series and different methods • Individual Series » Direct Method » Shortcut Method • Discrete Series » Direct Method » Shortcut Method • Continuous Series » Direct Method » Shortcut Method » Step Deviation Method
  • 4. Individual Series - Direct Method Student A B C D E F G H I J Marks 2 7 10 8 6 3 5 4 5 0 The Problem – Calculate the arithmetic mean for the data given below 1. Write the sum in rows and column format.Student X A 2 B 7 C 10 D 8 E 6 F 3 G 5 H 4 I 5 J 0 2. Formula to find the arithmetic mean= = 2+7+10+8+6+3+5+4+5+0 10 = 50 10 = 5 Ans : The arithmetic mean is 5 50 ∑x Nis the number of observations N is the number of observations in our e.g. there are 10 students so N =10
  • 5. Individual Series: Shortcut Method Student A B C D E F G H I J Marks 2 7 10 8 6 3 5 4 5 0 2. Assume a Mean (A) = 2 1. Draw 2 columns ; a. Under X write the marks. b. dx = X-A 3. Formula to find the arithmetic mean = = 2 + 0+5+8+6+4+1+3+2+3(-2) 10 = 2 + 32-2 10 = 2+3 = 5 Ans : The arithmetic mean is 5 =2 + 30 10 X 2 7 10 8 6 3 5 4 5 0 A = 2 dx = X - A 2 -2 = 0 7- 2 = 5 10 - 2 = 8 8 - 2 = 6 6 - 2 = 4 3 -2 = 1 5 -2 = 3 4 -2 = 2 5 - 2 = 3 0 - 2= -2 30 = A + ∑dx / N
  • 6. Discrete Series- Direct method Marks Received by students 5 2 3 4 Frequency 4 6 8 6 Step 1. Column ‘x’ and put all the data of marks received by students in this column. Step 2. Column ‘’f and put all the data of frequency under this. Step 3. Third column ‘fx’ ; fx = f x X i.e multiply data in col. f with data in col. X. Step 4. Find ∑fx add all the data in column ‘ fx’ = 20+ 12 +24 +24 = 80 Step 5. Find ∑f Add all data in column ‘f’ = 4+6+8+6 = 24 Step 6 .Formula to find mean = (∑fx) (∑f) = 80/24 = 3.33 ; ANS = 3.33 x Marks Received by students 5 2 3 4 f Frequency 4 6 8 6 24 fx 4 x 5 = 20 6 x 2 = 12 8 x 3 = 24 6 x 4 = 24 80
  • 7. Discrete Series- Shortcut method Marks Received by students 5 2 3 4 Frequency 4 6 8 6 Step 1. Make a column ‘x’ and put all the data of marks received by students in this column. Step 2. Column ‘’f and put all the data of frequency under this. Step 3. Column Assume a no. A in our e.g. we have assumed A = 2 ‘dx’ ; dx = x -A Step 4. Find ∑fdx Multiply data in column ‘f’ with data in column ‘dx’. ∑fdx = sum of the column fdx = 32 Step 5. Find ∑f Add all data in column ‘f’ = 4+6+8+6 = 24 Step 6 . Formula = A + (∑fdx)/(∑f) = 2 + 32/24 = 3.33 ; ANS = 3.33 x Marks Received by students 5 2 3 4 f Frequency 4 6 8 6 A = 2 dx = x - A 5 - 2= 3 2 - 2= 0 3 - 2= 1 4 - 2= 2 fdx 4 x 3 = 12 6 x 0 = 0 8 x 1 = 8 6 x 2 = 12 24 32
  • 8. Continuous Series - Direct Method The following table shows wages of workers. Calculate the arithmetic mean. Wages 10 - 20 20-30 30 - 40 40 - 50 50 - 60 No. of Workers 8 9 12 11 6 The wages are given in a group series e.g. how many workers get wages between 10 to 20 Ans. 8. How many workers get wages between 20 and 30 Ans. 9. Here ‘X’ is the wages, but we cannot identify one number for ‘X’. So we need to find the ‘Mid Value’ of each group. e.g. To find the Mid value of the first group ‘10 – 20’ Formula to find the Mid Value L1 + L2/ 2 L1 = the first number in the group in our example it is ‘10’ L2 = the second number in the group, in our example it is ‘20 ‘ Divide by 2, because we need to divide into two halves so we know which number is in the middle. So the mid value (M.V) for the first group ‘10 – 20’ = 10 + 20 / 2 = 30 /2 = 15
  • 9. Arrange the numbers in the following manner Add a column “MV”(Mid Value) which will be your new ‘X’, and find the Mid Value X MV (Mid Value) 10+20/2 = 15 20+30/2 = 25 30+40/2= 35 40+50/2 = 45 50+60/2 = 55 Formula = ∑fx/ ∑fWages f No. of Workers 10 - 20 8 20-30 9 30 - 40 12 40 - 50 11 50 - 60 6 Add another column ‘fx’ i.e multiple value in column ‘f’ and the value in column ‘X’. fx 8 x 15 = 120 9 x 25 = 225 12 x 35 = 420 11 x 45 = 495 6 x 55 = 330 Find ∑f i.e (find the total of column ‘f’) Find ∑fx i.e (find the total of column ‘fx’) ∑f = 46 ∑fx 1590 = 1590 46 Answer = 34.56 Continuous Series - Direct Method.. Cont.….
  • 10. Continuous Series – Shortcut Method Wages 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 f No.of Workers 8 9 12 11 6 46 x Mid Value 10 + 20/2 = 15 20 + 30/2= 25 30 + 40 /2 = 35 40 + 50/2 = 45 50 + 60/2 = 55 Assume A = 15 dx = x - A dxf 15 - 15 = 0 25 - 15= 10 35 - 15= 20 45 - 15= 30 55 - 15= 40 1.Draw the 3 columns similar to the direct method i.e Wages, f (no.of workers and x-Midvalue) 2. Next assume a no. A (preferably from column’x’). In our eg we have assumed A = 15. 3. Find dx, dx = x – A. 4. Find fdx ; Multiply the answer in dx column with the 2nd column ‘f’. 5. Formula to find the arithmetic mean = A + ∑fdx ∑f = A + ∑fdx ∑f = 15 + 900 46 Answer = 34.56 fdx 0 x 8 = 0 10 x 9 = 90 20 x 12 = 240 30 x 11 = 330 40 x 6 = 240 900
  • 11. Continuous Series – Step deviation Method 1.Draw the columns similar to the shortcut method i.e Wages, f, x and dx 2. Next assume a no. C. In our eg we have assumed c = 10. 3. Find dx’, dx’= dx /c. 4. Find fdx’ ; Multiply the answer in dx’ column with the 2nd column ‘f’. 5. Formula to find the arithmethic mean = A + ∑fdx’ x c ∑f = A + ∑fdx’ x c ∑f Answer = 34.56 Wages 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 f No.of Workers 8 9 12 11 6 46 x Mid Value 10 + 20/2 = 15 20 + 30/2= 25 30 + 40 /2 = 35 40 + 50/2 = 45 50 + 60/2 = 55 Assume A = 15 dx = x - A dxf 15 - 15 = 0 25 - 15= 10 35 - 15= 20 45 - 15= 30 55 - 15= 40 Assume C= 10 dx' = dx/c 0/10 = 0 10/10= 1 20/10= 2 30/10= 3 40/10= 4
  • 12. Individual Series Direct Method : Shortcut Method : Discrete Series Direct Method : = ∑fx ∑f Shortcut Method : = A + ∑fdx ∑f Continuous Series Direct Method Shortcut Method Step Deviation X X dx X f dx fdx X f fx X f x(M.V) fx No. of Boxes x f x (M.V) dx fdx x f x (M.V) dx dx' fdx'