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Look at this set of $6$ numbers: $\newline$ $9, 1, 3, 2, 8, 1$ $\newline$ How would the mean change if the number $2$ replaced the number $8$ 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

6

numbers:

\newline

9, 1, 3, 2, 8, 1

\newline

How would the mean change if the number

2

replaced the number

8

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Calculate Mean: Step $1$ : Calculate the mean of the original set of numbers: $9, 1, 3, 2, 8, 1$ . Sum of original numbers = $9 + 1 + 3 + 2 + 8 + 1 = 24$ . Number of elements = $6$ . Original mean = $24 / 6 = 4$ .
Replace Number: Step $2$ : Replace the number $8$ with $2$ in the set, resulting in the new set: $9, 1, 3, 2, 2, 1$ . $\newline$ Sum of new numbers = $9 + 1 + 3 + 2 + 2 + 1 = 18$ . $\newline$ New mean = $\frac{18}{6} = 3$ .
Compare Means: Step $3$ : Compare the original mean and the new mean. $\newline$ Original mean = $4$ . $\newline$ New mean = $3$ . $\newline$ Since $3$ is less than $4$ , the mean decreases.

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