Multiple choice

A data set of 25 distinct numbers has a mean of 40 and a median of 40. A new data set is created by adding 5 to each number greater than the median and subtracting 5 from each number less than the median. Which of the following measures does NOT remain unchanged in both the original and new data sets?

  1. Median

  2. Mean

  3. Sum of the 25 numbers

  4. Standard deviation
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D Correct answer
Explanation

Adding 5 to values above the median and subtracting 5 from values below the median changes the spread of the data, thereby increasing the standard deviation, while the mean and median remain unchanged due to symmetry.

AI explanation

In the new data set, 5 is added to the upper half of the numbers and 5 is subtracted from the lower half, keeping the overall sum and therefore the mean exactly the same at 40. Because the middle value is unchanged, the median also remains unchanged at 40. However, since the values are shifted further away from the mean in both directions, the spread of the data increases, meaning the standard deviation changes.

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