Question

Question
Evan is doing research, and he estimated the population mean using four random samples. Evan accidentally erased one of the sample means. What is the missing sample mean if the estimated population mean is 14.1 and the sample means are 14.8, 13.2, 14.6?(1 point)
Responses

12.4
12.4

13.8
13.8

14.6

Answer 1

To find the missing sample mean, we can use the formula for the average of the sample means:

\[
\text{Estimated population mean} = \frac{\text{Sum of sample means}}{\text{Number of samples}}
\]

Let \( x \) be the missing sample mean. The estimated population mean is given as 14.1, and the known sample means are 14.8, 13.2, and 14.6. There are a total of 4 samples.

We can set up the equation:

\[
14.1 = \frac{14.8 + 13.2 + 14.6 + x}{4}
\]

First, we need to calculate the sum of the known sample means:

\[
14.8 + 13.2 + 14.6 = 42.6
\]

Now substitute this sum into the equation:

\[
14.1 = \frac{42.6 + x}{4}
\]

To eliminate the fraction, multiply both sides by 4:

\[
4 \times 14.1 = 42.6 + x
\]

Calculating \( 4 \times 14.1 \):

\[
56.4 = 42.6 + x
\]

Now, solve for \( x \):

\[
x = 56.4 - 42.6
\]
\[
x = 13.8
\]

Thus, the missing sample mean is **13.8**.