In this power point calculation of arithmetic mode is explained for individual observation, discrete series, continuous series

1. Calculation of
Mode
SUBMITTED BY
DR. SUNITA OJHA
ASSISTANT PROFESSOR
SURESH GYAN VIHAR UNIVERSITY

2. Mode
• It is repeated the highest number of times in the series by definition
• The mode of a distribution is the value at the point around which the items tend to
be most heavily concentrated.
• The main feature of mode is that it is the size of that item which has the maximum
number frequency.
1. Calculation of mode in a series of individual observations:
• The value occurring maximum number of times are the modal values.
Example1. Find the mode of the following data relating to the weights of a sample of
experimental animals
S.No. 1 2 3 4 5 6 7 8 9 10
Weight 10 11 10 12 12 11 9 8 11 11

3. Weight No. of
animals
8 1
9 1
10 2
11 4
12 1
13 1
• Since the item 11 occurs the maximum number of
times i.e. 4 times, the modal value is 11.
• If two values have the maximum frequency, the
series is bimodal.
2. Calculation of mode in a discrete series.
• Mode can be determined by looking to that
variable around which the items are most heavily
concentrated.
Value 6 8 10 12 14 16 18 20 22 24
Frequency 20 30 40 40 55 60 55 20 15 25
• In the above data modal value is 16, because it occurs the maximum no.
of times i.e. 60 times

4. • However, the values on the either side of 16 have also large frequencies.
• In such cases, it is desirable to prepare a grouping table and an analysis table.
• Grouping Table has six columns. Frequencies are added in two’s or three’s
• In column 1, maximum frequency is marked.
• In column 2, frequencies are added in two’s (1+2, 3+4, 5+6……).
• In column 3, frequencies are added in two’s leaving the first frequency
(2+3, 4+5, 6+7…).
• In column 4, frequencies are added in three’s (1+2+3, 4+5+6, 7+8+9…).
• In column 5, frequencies are added in three’s leaving the first frequency
(2+3+4, 5+6+7, 8+9+10,….).
• In column 6, frequencies are added in three’s leaving the first two
frequencies (3+4+5, 6+7+8, 9+10+11,….).
• Mark the maximum frequency in each column.
• Prepare the analysis table to find out the exact value of the modal class.

5. Variable (x) 2 4 6 8 10 12 14 16 18 20
Frequency
(f)
15 20 25 27 30 20 15 21 10 11
Grouping Table
Variable
(x)
Col.1 Col.2 Col.3 Col.4 Col.5 Col.6
2 15 35 60
4 20 45 72
6 25 52 82
8 27 57 77
10 30 50 65
12 20 35 56
14 15 27 46
16 21 22 42
18 10 21
20 11

6. Analysis Table
Col.
No.
2 4 6 8 10 12 14 16 18 20
1 1
2 1 1
3 1 1
4 1 1 1
5 1 1 1
6 1 1 1
Total 1 3 5 4 1
Variable (x)
• In this example the modal value is 10. because it shows maximum frequency.
• However, the concentration of the items is more on the either side of this value.
• After grouping analysis the modal value is found to be 8 and not 10.
• Mode is affected by the frequencies of the neighboring items.

7. 2. Calculation of mode in a discrete series.
Mode can be calculated by the formula:
𝑀𝑜𝑑𝑒 = 𝐿 +
𝑓1 − 𝑓0
2𝑓1 − 𝑓𝑜 − 𝑓2
× 𝑖
L= Lower limit of the modal class
f0= frequency of the class preceding modal class
f1= frequency of modal class
f2= frequency of the class succeeding modal class.
i= Class interval

8. Here modal class is 30-60.
L= 30
f0=21
f1= 51
f2= 35
i= 10
Mode= 30+(51-21/2*51-21-35)10
=30+6.52
=36.52
Classes Frequency
0-10 5
10-20 21
20-30 51
30-40 35
40-50 18
50-60 30

9. References
Khan, I. A., & Khanum, A. (1994). Fundamentals of biostatistics. Ukaaz.
Sharma, A. K. (2005). Text book of biostatistics I. Discovery Publishing House.
Daniel, W. W., & Cross, C. L. (2018). Biostatistics: a foundation for analysis in
the health sciences. Wiley.