The following data reflect the number of customers who return merchandise for a refund on Monday.Note these data reflect the population of all 10 Mondays for which data are available. Assume that this same exact pattern of data were replicated for the next ten days.How would this affect the standard deviation for the new population with 20 items?
A)The standard deviation would be doubled.
B)The standard deviation would be cut in half.
C)The standard deviation would not be changed.
D)There is no way of knowing the exact impact without knowing how the mean is changed.

Question

The following data reflect the number of customers who return merchandise for a refund on Monday.Note these data reflect the population of all 10 Mondays for which data are available.  Assume that this same exact pattern of data were replicated for the next ten days.How would this affect the standard deviation for the new population with 20 items?
A)The standard deviation would be doubled. 
B)The standard deviation would be cut in half. 
C)The standard deviation would not be changed. 
D)There is no way of knowing the exact impact without knowing how the mean is changed.

Quizplus · Accepted Answer

Since the data pattern is the same for the next ten days, the standard deviation would not be changed as it is solely dependent on the variability of the data itself and not the sample size. The formula for calculating standard deviation takes into account the sum of the differences between each data point and the mean, and since this sum remains the same regardless of the sample size, the standard deviation would not be affected.

The Following Data Reflect the Number of Customers Who Return