Question

Evan is doing research and 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, and 14.6?

Answer 1

To find the missing sample mean, we can use the formula for the estimated population mean, which is the average of all the sample means.

Given:

- Estimated population mean (M) = 14.1
- Sample means = 14.8, 13.2, 14.6, and one missing sample mean (let's call it \( x \))

The formula for the mean of the four sample means is:

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

Setting this equal to the estimated population mean gives us:

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

Now let's calculate the sum of the known sample means:

\[
14.8 + 13.2 + 14.6 = 42.6
\]

Now we can substitute this 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 the left side:

\[
56.4 = 42.6 + x
\]

Now, solve for \( x \):

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

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