Distribution Shape Statistics Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumClassify each distribution shape: (a) Test scores cluster around 75 with equal tails. (b) Marathon finish times have a peak at 4 hours with a long tail for slower runners. (c) Ages at a family reunion show peaks at 10 and 40.
Solution
- 1 Step 1: (a) Equal tails around a central peak — symmetric (bell-shaped).
- 2 Step 2: (b) Peak with a long right tail — right-skewed.
- 3 Step 3: (c) Two peaks — bimodal.
Answer
(a) Symmetric, (b) Right-skewed, (c) Bimodal.
Recognising distribution shapes helps us choose appropriate summary statistics and understand the underlying data patterns.
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 3 mediumA histogram of exam scores is left-skewed. What does this tell us about the relationship between the
Example 4 mediumA distribution has most values near the high end, with a tail stretching toward smaller values. What