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Look at this set of $7$ numbers: $\newline$ $81, 97, 36, 75, 55, 88, 47$ $\newline$ How would the median change if the number $81$ were added to 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

7

numbers:

\newline

81, 97, 36, 75, 55, 88, 47

\newline

How would the median change if the number

81

were added to the set?

\newline

Choices:

\newline

(A) increase

\newline

(B) decrease

\newline

(C) no change

Arrange Numbers Ascending: Step $1$ : Arrange the original set of numbers in ascending order. $\newline$ Original set: $81, 97, 36, 75, 55, 88, 47$ $\newline$ Ascending order: $36, 47, 55, 75, 81, 88, 97$
Find Original Set Median: Step $2$ : Find the median of the original set. $\newline$ Since there are $7$ numbers, the median is the fourth number in the ordered list. $\newline$ Median of original set: $75$
Add Number $81$ : Step $3$ : Add the number $81$ to the set and arrange it in ascending order. $\newline$ New set: $81, 97, 36, 75, 55, 88, 47, 81$ $\newline$ Ascending order: $36, 47, 55, 75, 81, 81, 88, 97$
Find New Set Median: Step $4$ : Find the median of the new set. $\newline$ Since there are now $8$ numbers, the median is the average of the fourth and fifth numbers. $\newline$ Median of new set: $(75 + 81) / 2 = 78$

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