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Look at this set of $6$ numbers: $\newline$ $45, 55, 62, 31, 35, 87$ $\newline$ How would the median change if the number $92$ 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

6

numbers:

\newline

45, 55, 62, 31, 35, 87

\newline

How would the median change if the number

92

were added to 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: $45, 55, 62, 31, 35, 87$ $\newline$ Ascending order: $31, 35, 45, 55, 62, 87$
Find Median of Original Set: Step $2$ : Find 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. $\newline$ Median = $(45 + 55) / 2 = 50$
Add Number $92$ and Arrange: Step $3$ : Add the number $92$ to the set and arrange it in ascending order. $\newline$ New set: $31, 35, 45, 55, 62, 87, 92$
Find Median of New Set: Step $4$ : Find the median of the new set. $\newline$ Since there are now $7$ numbers, the median is the $4$ th number. $\newline$ Median $= 55$

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