The 153 heights of males in a data set have a standard deviation of 7.08 cm. What is the variance of their heights? Be sure to include the appropriate units with the result. DO NOT ROUND

The variance of a data set is the square of the standard deviation. Given that the standard deviation (σ) of the heights is 7.08 cm, the formula for variance (σ²) is:

\[
\text{Variance} = \sigma^2 = (7.08 \, \text{cm})^2 = 50.1264 \, \text{cm}^2
\]

Thus, the variance of their heights is **50.1264 cm²**.

Would you like further details or have any questions?

Here are 5 related questions for deeper exploration:
1. How does variance differ from standard deviation conceptually?
2. If the standard deviation were in inches instead of cm, how would that affect the variance?
3. What is the significance of high versus low variance in a data set?
4. How would adding a constant to each value in the data set affect the variance?
5. Can variance ever be negative? Why or why not?

**Tip:** Always remember that variance uses squared units, unlike standard deviation which is in the same units as the data.

The 153 heights of males in a data set have a standard deviation of 7.08 cm. What is the variance of their heights? Be sure to include the appropriate units with the result. DO NOT ROUND.

Find the variance for a dataset of 153 male heights with a standard deviation of 7.08 cm. This statistical problem teaches the relationship between standard deviation and variance, using the formula Variance = (Standard Deviation)^2. Learn more with detailed steps and explanations, suitable for Grades 9-12.

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