2. 2
SKEWNESS
•
Distributions (aggregations of observations) can be spread evenly around both
sides of the central tendency, like so:
1 2 3 4 5 6 7 8 9
1
2
3
4
5
Such distributions are considered symmetrical with no skew.
5
5
Mean =
Median =
3. 3
SKEWNESS
•
As scores are weighted and distribute unevenly around the median, the mean is
“pulled” toward the extreme outlier and it diverges away from the median.
1 2 3 4 5 6 7 8 9
1
2
3
4
5
7
5
Mean =
Median =
2120
4. SKEWNESS
•
When the outlying scores are on the higher end of the scale the distribution
becomes positively skewed.
1 2 3 4 5 6 7 8 9
1
2
3
4
5
2120
+
5. SKEWNESS
•
When the outlying scores are on the lower end of the scale the distribution
becomes negatively skewed.
1 2 3 4 5 6 7 8 9
1
2
3
4
5
2120
_
9. 9
kurtosis
•
Distributions of data and probability distributions are not all the same shape.
Some are asymmetric and skewed to the left or to the right. Many times,
there are two values that dominate the distribution of values.
Kurtosis is the measure of the peak of a distribution, and indicates how high the distribution is around the mean.
10. Types of kurtosis
Mesokurtic
A distribution
identical to the
normal distribution
Leptokurtic
A distribution that is
more peaked
than normal
Platykurtic
A distribution that is
less peaked than
normal