Which data set can you add to the data shown to increase the median of the data? 5 13 11 14 7 A.{2, 19} B.{6, 12, 16} C.{6, 11, 15} D.{3, 4, 14}

Question

Mathematics

Mckee

13 January, 11:52

Which data set can you add to the data shown to increase the median of the data? 5 13 11 14 7 A.{2, 19} B.{6, 12, 16} C.{6, 11, 15} D.{3, 4, 14}

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Answers (1)

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Rebecca Mcguire · Answer 1

The median is the middle number in a set of data, or the arithmetic mean of two middle numbers if there is even number of elements in the set.

Sort the numbers from least to greatest:

5, 7, 11, 13, 14

The median is 11.

A. If you add {2, 19}:

2, 5, 7, 11, 13, 14, 19

The median is 11.

B. If you add {6, 12, 16}:

5, 6, 7, 11, 12, 13, 14, 16

The median is the mean of 11 and 12.

(11+12) / 2=23/2=11.5

The median is 11.5.

C. If you add {6, 11, 15}:

5, 6, 7, 11, 11, 13, 14, 15

The median is the mean of 11 and 11.

(11+11) / 2=22/2=11

The median is 11.

D. If you add {3, 4, 14}:

3, 4, 5, 7, 11, 13, 14, 14

The median is the mean of 7 and 11.

(7+11) / 2=18/2=9

The median is 9.

In A and C the median of the new data is the same as the original median, in D it's less than the original median, only in B it's greater.

You can add {6, 12, 16} to the data to increase the median.

The answer is B.