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Look at this set of $10$ numbers: $\newline$ $26, 60, 50, 50, 10, 30, 26, 47, 32, 27$ $\newline$ How would the median change if the number $39$ replaced the number $60$ 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

26, 60, 50, 50, 10, 30, 26, 47, 32, 27

\newline

How would the median change if the number

39

replaced the number

60

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: $26, 60, 50, 50, 10, 30, 26, 47, 32, 27$ $\newline$ Sorted set: $10, 26, 26, 27, 30, 32, 47, 50, 50, 60$
Calculate original set median: Step $2$ : Calculate the median of the original set. $\newline$ Since there are $10$ numbers, the median is the average of the $5$ th and $6$ th numbers. $\newline$ Median = $(30 + 32) / 2 = 31$
Replace number $60$ with $39$ : Step $3$ : Replace the number $60$ with $39$ in the set and sort it. $\newline$ New set: $26, 39, 50, 50, 10, 30, 26, 47, 32, 27$ $\newline$ Sorted new set: $10, 26, 26, 27, 30, 32, 39, 47, 50, 50$
Calculate new set median: Step $4$ : Calculate the median of the new set. $\newline$ Since there are still $10$ numbers, the median is the average of the $5$ th and $6$ th numbers. $\newline$ Median $= (30 + 32) / 2 = 31$

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