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Look at this set of $10$ numbers: $\newline$ $27, 39, 50, 33, 81, 30, 13, 67, 66, 28$ $\newline$ How would the median change if the number $37$ replaced the number $13$ in the set? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease $\newline$ (C)no change

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Changes in mean, median, mode, and range

Full solution

Q. Look at this set of

10

numbers:

\newline

27, 39, 50, 33, 81, 30, 13, 67, 66, 28

\newline

How would the median change if the number

37

replaced the number

13

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Arrange numbers in ascending order: Step $1$ : Arrange the original set of numbers in ascending order. $\newline$ Original set: $27, 39, 50, 33, 81, 30, 13, 67, 66, 28$ . $\newline$ Ordered set: $13, 27, 28, 30, 33, 39, 50, 66, 67, 81$ .
Identify median of ordered set: Step $2$ : Identify the median of the original ordered set. $\newline$ Since there are $10$ numbers, the median is the average of the $5$ th and $6$ th numbers. $\newline$ Median = $(33 + 39) / 2 = 36$ .
Replace number $13$ with $37$ : Step $3$ : Replace the number $13$ with $37$ in the original set and reorder it. $\newline$ New set: $27, 39, 50, 33, 81, 30, 37, 67, 66, 28$ . $\newline$ Ordered new set: $27, 28, 30, 33, 37, 39, 50, 66, 67, 81$ .
Identify median of new ordered set: Step $4$ : Identify the median of the new ordered set. $\newline$ Since there are still $10$ numbers, the median is the average of the $5$ th and $6$ th numbers. $\newline$ Median = $(37 + 39) / 2 = 38$ .

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