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Rachel has the following data: $\newline$ $15, 12, 7, p, 5, 7$ $\newline$ If the range is $10$ , which number could $p$ be? $\newline$ Choices: $\newline$ $(A)$ $5$ $\newline$ $(B)$ $16$

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Mean, median, mode, and range: find the missing number

Full solution

Q. Rachel has the following data:

\newline

15, 12, 7, p, 5, 7

\newline

If the range is

10

, which number could

p

be?

\newline

Choices:

\newline

(A)

5

\newline

(B)

16

Calculate Range: Calculate the range of the given numbers excluding $p$ . The range is the difference between the maximum and minimum values. $\newline$ Max value without $p$ = $15$ , Min value without $p$ = $5$ . $\newline$ Range = Max - Min = $15 - 5 = 10$ .
Determine Impact of $p=16$ : Since the range with $p$ included must also be $10$ , $p$ must either increase the maximum value or decrease the minimum value but still keep the range as $10$ .
Check if $p = 16$ affects the range:
New Max = $16$ , New Min = $5$ , New Range = $16 - 5 = 11$ .
Determine Impact of $p=5$ : Check if $p = 5$ affects the range: $\newline$ New Max = $15$ , New Min = $5$ , New Range = $15 - 5 = 10$ .

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