How will adding the value 200 affect the mean and median of the data set 10, 15, 17, 17, 19, 20?

A.
The mean increases and the median stays the same.

B.
The mean and the median increase by the same amount.

C.
The mean increases less than the median increases.

D.
The median increases and the mean stays the same.

Question

jubileebug jubileebug

18-06-2015
Mathematics

contestada

How will adding the value 200 affect the mean and median of the data set 10, 15, 17, 17, 19, 20?

A.
The mean increases and the median stays the same.

B.
The mean and the median increase by the same amount.

C.
The mean increases less than the median increases.

D.
The median increases and the mean stays the same.

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Christinecoconnor Christinecoconnor · Answer 1 · 2015-06-18T01:32:41+02:00

The median of the original set is 17 (the two middle numbers are both 17) and the median of the new set is also 17. I could stop here, because only one option says that the median stays the same, but I'll show how the mean increases. The mean of the original set is (10+15+17+17+19+20)/6, which is 98/6, which is 16 and 1/3. The mean of the new set is (10+15+17+17+19+20+200)/7, which is 298/7, which is 42 and 4/7. Therefore, the mean increases and the median stays the same, meaning answer A is correct.