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Look at this set of $8$ numbers: $\newline$ $23, 74, 31, 19, 54, 47, 23, 25$ $\newline$ How would the median change if the number $63$ replaced the number $25$ 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

23, 74, 31, 19, 54, 47, 23, 25

\newline

How would the median change if the number

63

replaced the number

25

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: $23, 74, 31, 19, 54, 47, 23, 25$ $\newline$ Ascending order: $19, 23, 23, 25, 31, 47, 54, 74$
Find Median of Original Set: Step $2$ : Find 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. $\newline$ Median = $(25 + 31) / 2 = 28$
Replace Number and Arrange: Step $3$ : Replace the number $25$ with $63$ and arrange the new set in ascending order. $\newline$ New set: $23, 74, 31, 19, 54, 47, 23, 63$ $\newline$ Ascending order: $19, 23, 23, 31, 47, 54, 63, 74$
Find Median of New Set: Step $4$ : Find the median of the new set. $\newline$ Since there are still $8$ numbers, the median is the average of the $4$ th and $5$ th numbers. $\newline$ Median = $(31 + 47) / 2 = 39$

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