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Look at this set of $10$ numbers: $\newline$ $8, 7, 8, 5, 8, 3, 7, 1, 4, 1$ $\newline$ How would the median change if the number $6$ 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

10

numbers:

\newline

8, 7, 8, 5, 8, 3, 7, 1, 4, 1

\newline

How would the median change if the number

6

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: $8, 7, 8, 5, 8, 3, 7, 1, 4, 1$ $\newline$ Ascending order: $1, 1, 3, 4, 5, 7, 7, 8, 8, 8$
Calculate Median of Original Set: Step $2$ : Calculate the median of the original set. $\newline$ Since there are $10$ numbers, the median will be the average of the $5$ th and $6$ th numbers. $\newline$ $5$ th number = $5$ , $6$ th number = $7$ $\newline$ Median = $(5 + 7) / 2 = 6$
Add Number $6$ and Arrange: Step $3$ : Add the number $6$ to the set and arrange it in ascending order. $\newline$ New set: $1, 1, 3, 4, 5, 6, 7, 7, 8, 8, 8$ $\newline$ Ascending order: $1, 1, 3, 4, 5, 6, 7, 7, 8, 8, 8$
Calculate Median of New Set: Step $4$ : Calculate the median of the new set. $\newline$ Since there are now $11$ numbers, the median will be the $6$ th number. $\newline$ $6$ th number = $6$

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