Question

use the range and the mean to find the missing numbers in each ordered data set. 18. 23, 24, _, 29, 33, _ range = 15 mean = 29 19. _, _, 84, 86, 86, 88, 91 range = 29 mean = 82

Explanation:

Step1: Recall range and mean formulas

Range = Largest - Smallest; Mean = $\frac{\text{Sum of all numbers}}{\text{Number of numbers}}$

Step2: Solve for 18

Let the missing numbers be $x$ and $y$ in order. Given range = 15 and smallest number is 23, so largest number $y=23 + 15=38$.
The mean of 23, 24, $x$, 29, 33, 38 is 29. The sum of these numbers is $29\times6 = 174$.
The sum of the known numbers is $23+24 + 29+33+38=147$. So $x=174 - 147=27$.

Step3: Solve for 19

Let the missing numbers be $a$ and $b$ in order. Given range = 29 and largest number is 91, so smallest number $a=91 - 29 = 62$.
The mean of $a$, $b$, 84, 86, 86, 88, 91 is 82. The number of numbers is 7, so the sum is $82\times7=574$.
The sum of the known numbers is $62+84 + 86+86+88+91=497$. So $b=574 - 497 = 77$.

Answer:

1. 27, 38
2. 62, 77