Distribution Shape Statistics Example 1
Follow the full solution, then compare it with the other examples linked below.
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.
Solution
- 1 Step 1: A peak on the left with a long right tail is a right-skewed (positively skewed) distribution.
- 2 Step 2: In right-skewed distributions, the few high values pull the mean to the right.
- 3 Step 3: Therefore, the mean is larger than the median.
Answer
Right-skewed distribution. Mean > Median.
Distribution shape affects the relationship between mean and median. In right-skewed data, extreme high values inflate the mean, making it larger than 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 2 medium
Classify 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
Example 4 mediumA distribution has most values near the high end, with a tail stretching toward smaller values. What