Histogram Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumA histogram of household incomes is skewed right. Describe what this means and explain why the mean would be greater than the median for this distribution.
Solution
- 1 Skewed right interpretation: the majority of households have moderate income, but a long tail extends to the right (a few very high incomes)
- 2 Effect on mean: the mean is pulled toward the tail by high-income outliers, increasing it above the center of most data
- 3 Effect on median: the median is the middle value — unaffected by extreme values in the tail
- 4 Conclusion: mean > median in right-skewed distributions because the mean is not resistant to outliers
Answer
Right skew means a long right tail. Mean > median because high values pull the mean rightward.
Shape of a histogram directly influences summary statistics. Right-skewed distributions arise naturally in economics (income, wealth) and biology (survival times). The median is preferred for center in skewed distributions because it is resistant to extreme values.
About Histogram
A histogram is a bar chart of a frequency distribution where bars represent count or density of data within consecutive equal-width intervals (bins).
Learn more about Histogram →More Histogram Examples
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