Which of the following sets of data will have the smallest $standarddeviation$?

• A. $0,5,10,15,20$
• B. $2,2,2,2,2$
• C. $4,8,12,16,20$
• D. $1,3,5,7,9$

Answer: (B)

Verified step by step guidance

1. Recall that the standard deviation measures the amount of variation or dispersion in a set of data values. A smaller standard deviation means the data points are closer to the mean.
2. Calculate the mean (average) of each data set using the formula: \(\text{mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the data points and \(n\) is the number of points.
3. For each data set, find the squared differences from the mean: \((x_i - \text{mean})^2\) for each data point.
4. Calculate the variance by averaging these squared differences: \(\text{variance} = \frac{\sum (x_i - \text{mean})^2}{n}\).
5. The standard deviation is the square root of the variance: \(\text{standard deviation} = \sqrt{\text{variance}}\). Compare the standard deviations of each set to determine which is smallest.