Distribution Shape Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
mediumA distribution has most values near the high end, with a tail stretching toward smaller values. What is the shape, and how do the mean and median compare?
Solution
- 1 Step 1: A tail toward smaller values means the distribution is left-skewed.
- 2 Step 2: In a left-skewed distribution, the lower tail pulls the mean below the median, so mean < median.
Answer
The distribution is left-skewed, and the mean is less than the median.
Skewness changes how the mean behaves relative to the median. A long tail on the low side pulls the mean downward more than it affects the median.
About Distribution Shape
Distribution shape describes the overall pattern of how data values are spread when displayed in a histogram or dot plot. Common shapes include symmetric (bell curve), skewed left, skewed right, uniform (all values equally common), and bimodal (two peaks).
Learn more about Distribution Shape →More Distribution Shape Examples
Example 1 medium
A histogram of household incomes in a city shows a peak on the left with a long tail extending to th
Example 2 mediumClassify each distribution shape: (a) Test scores cluster around 75 with equal tails. (b) Marathon f
Example 3 mediumA histogram of exam scores is left-skewed. What does this tell us about the relationship between the