The weights of a set of moving boxes on a truck have a mean of 22 poun

gmatophobia
Can you please explain this problem ?

plus, let say SD in this problem is 4 then the new SD of the boxes still increase or remain the same ?

AnujL Standard deviation denotes how dispersed the data set is with respect to the mean.

In this question, we know that the mean weight of all the boxes is 22 pounds. The heavier box is 26 pounds (4 pounds above the mean) and the lighter box is 18 pounds (4 pounds below the mean). Hence after the two boxes that were added, the mean does not change and the mean of all the boxes is still 22 pounds.

Consider this - You've $22 with you, one friend gives you $4 and you lend $4 to another friend of yours. After both transactions, you will still have $22 with you.

Now back to the question - So after the two boxes are added the mean is still 22 pounds, however, we have added two data points which lie at some distance away from the mean. Hence the data set is now more dispersed and the SD increases.

Note:
1) The original value of standard deviation is not of any relevance to this question. So whether you take the original SD as 3, 4, or 2, the analysis and the behavior that the standard deviation increases remain the same.
2) We were able to arrive at the conclusion only because the value of the mean didn't change.