Question

A dieter recorded the number of calories he consumed at lunch for one week. As you can​ see, a mistake was made on one entry. The calories are listed in increasing order below.

349, 371, 386, 398, 412, 4190

When the error is corrected by removing the extra​ 0, will the mean​ change? Will the​ median? Explain without doing any calculation.

Answer 1

Correcting the calorie entry will change the mean but not the median of the data set since the corrected value does not affect the middle value in the ordered list.

Step-by-step explanation:

The student asks if removing the extra zero from an entry in a recorded list of calorie counts will change the mean and the median of the data set.

Yes, correcting the error by removing the extra 0 from 4190 to make it 419 will change the mean of the caloric intake.

However, the median will not change because the median is the middle value of an ordered list, and correcting the entry does not affect the middle value when the data is sorted in increasing order.

The corrected calorie numbers are 349, 371, 386, 398, 412, and 419, with 398 as the median both before and after the correction.