Question to test your Standard Deviation knowledge

Question

Refer to the dataset given below. First, determine the range of the dataset. Then, apply the range rule of thumb to estimate the standard deviation. Finally, compare this estimate with the actual standard deviation computed from the entire dataset.
Male Athletes' Running Speeds (m/s):
8.5, 9.2, 9.8, 8.9, 10.1, 9.5, 8.7, 9.3, 9.0, 9.7
Female Athletes' Running Speeds (m/s):
7.4, 7.8, 8.1, 7.9, 8.3, 7.6, 8.0, 7.7, 7.5, 8.2
Does the variation in speeds appear to differ between male and female athletes?

Accepted Answer

The estimated standard deviation is significantly lower than the actual standard deviation, suggesting that the dataset has a non-uniform spread with substantial variation.

Yes, male athletes exhibit greater variation.

Answer

The estimated standard deviation closely matches the actual standard deviation, meaning the range rule of thumb provides a reasonable approximation.No, both groups show approximately equal variation.

Answer

The estimated standard deviation is significantly higher than the actual standard deviation, indicating that the dataset contains an outlier affecting the range.Female athletes have greater variation.

Answer

The estimated and actual standard deviations differ slightly, but both values suggest a similar level of variation in the dataset.The variations are indistinguishable due to sample size limitations.

Standard Deviation: Videos & Practice Problems