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Look at this set of $8$ numbers: $\newline$ $86, 37, 75, 71, 35, 86, 34, 91$ $\newline$ How would the median change if the number $85$ replaced the number $34$ 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

86, 37, 75, 71, 35, 86, 34, 91

\newline

How would the median change if the number

85

replaced the number

34

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: $34, 35, 37, 71, 75, 86, 86, 91$
Calculate Original Set Median: 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: $(71 + 75) / 2 = 73$ .
Replace Number $34$ with $85$ : Replace the number $34$ with $85$ and rearrange the set. $\newline$ New set: $35$ , $37$ , $71$ , $75$ , $85$ , $86$ , $86$ , $85$ $1$
Calculate New Set Median: Calculate the median of the new set. $\newline$ The median is now the average of the $4$ th and $5$ th numbers: $(75 + 85) / 2 = 80$ .

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