The following data are from a simple random sample: 5, 8, 10, 7, 10, 14. What is the point estimate of the population standard deviation?

3.1

The correct answer is Option (1) → 3.1

Given sample data is 5, 8, 10, 7, 10, 14 and n = 6.

The point estimate of population mean is sample mean.

$∴\bar x=\frac{Σx_i}{n}=\frac{5+8 +10 + 7 + 10 + 14}{6}$

$=\frac{54}{6} = 9$

The point estimate of population standard deviation is sample standard deviation.

$∴s =\sqrt{\frac{∑(x_i-\bar x)^2}{n-1}}$

Now, $∑(x_i -\bar x)^2 = (5 - 9)^2 + (8-9)^2 + (10-9)^2 + (7-9)^2 + (10 − 9)^2 + (14 − 9)^2$

$= 16 +1 +1 + 4+1 +25$

$= 48$

$∴s =\sqrt{\frac{48}{6-1}}=\sqrt{\frac{48}{5}}=\sqrt{9.6}$

$⇒s=3.1$