Question to test your Standard Deviation knowledge

Question

Find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as "minutes") in your results. The following data represent the duration (in minutes) of workout sessions completed by a group of individuals at a fitness center over a week:
$30 comma 45 comma 60 comma 50 comma 40 comma 55 comma 70 comma 35 comma 65 comma 50 comma 42$
What do the results tell us about the variation in workout durations?

$30 comma 45 comma 60 comma 50 comma 40 comma 55 comma 70 comma 35 comma 65 comma 50 comma 42$

What do the results tell us about the variation in workout durations?

Accepted Answer

${Range = 40 minutes, Variance = 155.8 minutes}^{2}, Standard deviation = 12.48 minutes$

The workout durations show moderate variability, meaning they are somewhat spread out but not extremely different.

Answer

${Range = 40 minutes, Variance = 155.8 minutes}^{2}, Standard deviation = 12.48 minutes$

The workout durations show high variability, meaning that workout times differ significantly from person to person.

Answer

${Range = 40 minutes, Variance = 155.8 minutes}^{2}, Standard deviation = 12.48 minutes$

The workout durations have low variability, indicating that most workout times are close to the average.

Answer

${Range = 40 minutes, Variance = 155.8 minutes}^{2}, Standard deviation = 12.48 minutes$

There is no variation in the workout durations, as all values are nearly the same.