Distribution Shape Statistics Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
mediumA histogram of exam scores is left-skewed. What does this tell us about the relationship between the mean and median?
Solution
- 1 Step 1: In a left-skewed distribution, the tail extends to the left (low values).
- 2 Step 2: The few low values pull the mean downward, so mean < median.
Answer
In a left-skewed distribution, the mean is less than the median.
Skewness determines how the mean and median relate: left-skewed → mean < median, symmetric → mean ≈ median, right-skewed → mean > 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 4 mediumA distribution has most values near the high end, with a tail stretching toward smaller values. What