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Look at this set of $9$ numbers: $\newline$ $95, 86, 76, 37, 39, 86, 20, 44, 16$ $\newline$ How would the median change if the number $45$ replaced the number $16$ 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

9

numbers:

\newline

95, 86, 76, 37, 39, 86, 20, 44, 16

\newline

How would the median change if the number

45

replaced the number

16

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: $95, 86, 76, 37, 39, 86, 20, 44, 16$ $\newline$ Ascending order: $16, 20, 37, 39, 44, 76, 86, 86, 95$
Identify Original Median: Step $2$ : Identify the median of the original set. $\newline$ Since there are $9$ numbers, the median is the $5$ th number in the ordered set. $\newline$ Original median: $44$
Replace Number $16$ : Step $3$ : Replace the number $16$ with $45$ and reorder the set. $\newline$ New set: $95$ , $86$ , $76$ , $37$ , $39$ , $86$ , $20$ , $44$ , $45$ $\newline$ Ascending order: $20$ , $37$ , $39$ , $44$ , $45$ , $76$ , $86$ , $86$ , $95$
Identify New Median: Step $4$ : Identify the median of the new set. $\newline$ Since there are still $9$ numbers, the median is the $5$ th number in the ordered set. $\newline$ New median: $45$

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