Question

The height of a door is measured by four people and their measured values are 217.6 cm, 217.2 cm, 216.8 cm, and 217.9 cm. (a) What is the average value of these four measurements? (Enter your answer to the nearest tenths place.)
(b) What is the standard deviation for the four measurements?

Answer 1

Answer:

a) To the nearest tenth the average value of the measures is 217.4cm

b) The standard deviation for the four measurements is 0.415

Explanation:

The average is the result of adding all the values and dividing by the number of measures, in this case 4 then

$Average = \frac{217.6 + 217.2 + 216.8 + 217.9}{4}$

$Average = \frac{869.5}{4}$

$Average = 217.375$

a) To the nearest tenth the average value of the measures is 217.4cm

The standard deviation equals to the square root of the variance, and the variance is the adition of all the square of the difference between the measure and the average for each value divided by the number of measurements

So first, we must calculate the variance:

$Variance = \frac{(217.6-217.4)^2+(217.2-217.4)^2+(216.8-217.4)^2+(217.9-217.4)^2}{4}$.

$Variance = \frac{(0.2)^2+(-0.2)^2+(-0,6)^2+(0.5)^2}{4}$.

$Variance = \frac{0.04+0.04+0.36+0.25}{4}$.

$Variance = \frac{0.69}{4}$.

$Variance = 0.1725$.

This represent the difference between the average and the measurements.

Now calculate the standard deviation

Standard deviation  = $\sqrt{Variance}$

Standard deviation  = $\sqrt{0.1725}$

Standard deviation  = 0.415

b) The standard deviation for the four measurements is 0.415

This measure represent a standard way to know what is normal in this sample. so the differences between the average should be of ±0.415