Question

The following data is from a simple random sample: 15, 23, x, 37, 19, 32. If the point estimate of the population mean is 23, then the value of x is:

• A. 12
• B. 30
• C. 21
• D. 24

Answer 1

Answer: (A)

12

Answer 2

The sample mean is given by:
$\bar{x} = \frac{\text{Sum of all data points}}{\text{Number of data points}}.$

Substitute the given mean:
$23 = \frac{15 + 23 + x + 37 + 19 + 32}{6}.$

Simplify:
$23 \times 6 = 15 + 23 + x + 37 + 19 + 32.$
$138 = 126 + x \quad \Rightarrow \quad x = 138 - 126 = 12.$
Thus, $x = 12$.