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Look at this set of $8$ numbers: $\newline$ $97, 49, 91, 91, 69, 29, 87, 59$ $\newline$ How would the median change if the number $85$ replaced the number $49$ 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

97, 49, 91, 91, 69, 29, 87, 59

\newline

How would the median change if the number

85

replaced the number

49

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: $29, 49, 59, 69, 87, 91, 91, 97$ .
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: $(69 + 87) / 2 = 78$ .
Replace and Rearrange Data: Replace $49$ with $85$ in the data set and rearrange it. $\newline$ New set: $29$ , $59$ , $69$ , $85$ , $87$ , $91$ , $91$ , $97$ .
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: $(85 + 87) / 2 = 86$ .

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