Multiple choice

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

  1. Median

  2. Mean

  3. Sum of the numbers

  4. Standard Deviation
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D Correct answer
Explanation

Adding/subtracting a constant to values greater/less than the median changes the distribution spread, thus affecting the standard deviation. The mean, median, and sum remain unchanged because the changes are symmetric around the median.

AI explanation

Since there are 27 numbers, 13 numbers are above the median and 13 are below it. Adding 7 to the upper half and subtracting 7 from the lower half results in a net change of zero, keeping the sum and the mean unchanged. The median also remains at 33, but shifting the data points further away from the center alters the spread of the data. Therefore, the standard deviation does not remain the same.

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