Question

shoppers were surveyed about their spending for holiday shopping. the standard deviation of the amount shoppers spent was $125. which of the following is the best interpretation of this value?
fifty percent of the amount shoppers spent is above $125.
the middle half of the amount shoppers spent has a range that is $125 wide.
the amount shoppers spent typically varies by about $125 from the mean.
the difference between the largest and smallest amounts shoppers spent was $125.

Explanation:

• Option 1: The standard deviation is not related to the percentage of data above a certain value. The median divides data into 50 - 50, not the standard deviation.
• Option 2: The inter - quartile range (IQR) gives the range of the middle half of the data. The standard deviation is not the same as the IQR.
• Option 3: By definition, the standard deviation measures the typical amount by which data values vary from the mean. So, if the standard deviation of the amount shoppers spent is $125$, it means the amount shoppers spent typically varies by about $125$ from the mean.
• Option 4: The difference between the largest and smallest amounts is the range. The standard deviation is not the range.

Answer:

The amount shoppers spent typically varies by about $125$ from the mean.