In one study on heights, the median height was inches. A histogram of the data set was skewed to the left. Which of

the following values for the mean height is most plausible?

inches inches inches

69.8

70.4 72.2 67.5

The most plausible value for the mean is because when the data set

is skewed to the left, the mean is .

In a dataset that is skewed to the left (negatively skewed), the mean is typically less than the median because the longer tail on the left side pulls the mean downward.

Given the provided values:

- 69.8 inches
- 70.4 inches
- 72.2 inches
- 67.5 inches

Since the histogram is skewed to the left, the most plausible value for the mean should be less than the median height.

Without the exact median value provided, but assuming it's around the middle of the given choices (for example, between 70 and 72 inches), the mean would likely be:

- **67.5 inches**

This is the lowest value and is consistent with the characteristic of the mean being less than the median in a left-skewed distribution.

So, the most plausible value for the mean is **67.5 inches** because when the data set is skewed to the left, the mean is typically **less than the median**.

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Do you want more details or have any questions?

Here are some related questions to explore further:

1. How does skewness affect other measures of central tendency, like the mode?
2. Can the mean ever be greater than the median in a left-skewed distribution?
3. What happens to the mean and median in a perfectly symmetrical distribution?
4. How do outliers affect the mean in a left-skewed dataset?
5. What are other graphical representations that show data skewness effectively?

**Tip:** In skewed distributions, always consider the relationship between the mean and median to understand the direction of skewness!

In one study on heights, the median height was inches. A histogram of the data set was skewed to the left. Which of the following values for the mean height is most plausible? 69.8 inches, 70.4 inches, 72.2 inches, 67.5 inches. The most plausible value for the mean is because when the data set is skewed to the left, the mean is .

Explore how to determine the most plausible mean height in a dataset that is skewed to the left. Given values of 69.8 inches, 70.4 inches, 72.2 inches, and 67.5 inches, find out why 67.5 inches is the best estimate for the mean based on the relationship between the mean and median in skewed distributions. Suitable for Grades 9-12.

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