Practice Distribution Shape in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The overall pattern of how data values are spread, including whether the distribution is symmetric, skewed left, skewed right, uniform, or bimodal.
If you make a histogram, what shape emerges? A bell curve? A slope leaning one way? Two peaks? The shape tells you about what's typical and what's unusual in your data.
Example 1
mediumA histogram of household incomes in a city shows a peak on the left with a long tail extending to the right. Describe the shape and state whether the mean or median is likely larger.
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.
Example 3
mediumA histogram of exam scores is left-skewed. What does this tell us about the relationship between the mean and median?
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?