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Look at this set of $8$ numbers: $\newline$ $51, 69, 65, 77, 12, 37, 16, 21$ $\newline$ How would the median change if the number $31$ replaced the number $77$ 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

8

numbers:

\newline

51, 69, 65, 77, 12, 37, 16, 21

\newline

How would the median change if the number

31

replaced the number

77

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Arrange Data in Ascending Order: Arrange the original data set in ascending order. $\newline$ Original set: $12, 16, 21, 37, 51, 65, 69, 77$
Calculate Median of Original Set: Calculate the median of the original set. $\newline$ Since there are $8$ numbers, the median is the average of the $4$ th and $5$ th numbers: $(37 + 51) / 2 = 44$ .
Replace Value and Re-Arrange: Replace $77$ with $31$ in the set and arrange it in ascending order. $\newline$ New set: $12$ , $16$ , $21$ , $31$ , $37$ , $51$ , $65$ , $69$
Calculate Median of New Set: Calculate the median of the new set. $\newline$ The median is still the average of the $4$ th and $5$ th numbers: $(31 + 37) / 2 = 34$ .

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