Question

The mean of the given data set is $14$.
$8,9,12,p,21,22$
The steps to find the value $p$ are as follows:
Step 1: Find the sum of the observations. The sum of the observations is $72+p.$
Step 2: Find the number of observations. There are $6$ observations.
Step 3: $\frac{(72+p)}{6}=14,p=12$
Step 4: There is no error in the given steps.
Which of the following steps has an error, if any?

• A. Step 3
• B. Step 1
• C. Step 4
• D. Step 2

Answer 1

The correct option is C Step 4

Given data set: $8,9,12,p,21,22$
Mean $=14$
Sum of the observations $=8+9+12+p+21+22=72+p$
Mean $=\frac{\text{sum of the observations}}{\text{number of observations}}$
$14=\frac{72+p}{6}$
$14\times 6=\frac{72+p}{6}\times 6$
$84=72+p$
$p+72-72=84-72$
$p=12$
Hence, there is no error in the given steps.