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Look at this set of $6$ numbers: $\newline$ $97, 59, 47, 37, 64, 24$ $\newline$ How would the median change if the number $87$ replaced the number $64$ 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

6

numbers:

\newline

97, 59, 47, 37, 64, 24

\newline

How would the median change if the number

87

replaced the number

64

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: $24, 37, 47, 59, 64, 97$
Calculate Original Set Median: Calculate the median of the original set. $\newline$ Since there are $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers: $(47 + 59) / 2 = 53$
Replace Number with $87$ : Replace $64$ with $87$ in the set and arrange it in ascending order. $\newline$ New set: $24, 37, 47, 59, 87, 97$
Calculate New Set Median: Calculate the median of the new set. $\newline$ The median of the new set is also the average of the $3$ rd and $4$ th numbers: $(47 + 59) / 2 = 53$

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