Distribution (Intuition) Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyA distribution has mean 50 and median 65. Is this distribution symmetric, left-skewed, or right-skewed? Explain.
Solution
- 1 When mean < median, the mean is pulled toward lower values
- 2 This means there are some very low values pulling the mean down while the median stays near the bulk of the data
- 3 A long left tail (low values) creates this pattern — left-skewed distribution
Answer
Left-skewed (negatively skewed) because mean (50) < median (65).
The relative positions of mean and median reveal skewness: mean > median → right skew; mean < median → left skew; mean ≈ median → roughly symmetric. This works because the mean is pulled toward the tail more than the resistant median.
About Distribution (Intuition)
A distribution describes how data values are spread out across their range — which values occur, how often, and whether the data is symmetric or skewed.
Learn more about Distribution (Intuition) →More Distribution (Intuition) Examples
Example 1 easy
Describe the distribution of heights of adult men (approximately normally distributed with mean 70 i
Example 2 mediumCompare three distributions: (A) uniform (equal probability for all outcomes), (B) right-skewed (mos
Example 4 hardThe Central Limit Theorem says that sample means follow a normal distribution for large [formula], r