Question

`n = 20` , ∑
`x = 1570` , ∑
`x^2 = 125696` , minimum = 60, maximum = 100

Find s. Round your answer to one decimal place.

Estimate s by using the range rule-of-thumb. (If you can explain the range rule of thumb it'll be greatly appreciated).

Answer 1

Mean:-

`\\ \tt\hookrightarrow \overline{x}=(\sum x)/(n)=(1570)/(20)=78.5`

Standard deviation:-

• Two ways are available ,Let's do in both.

WAY-1(apply common formula)

`\\ \tt\hookrightarrow \sigma=\sqrt{(\sum x^2)/(n)-(\overline{x})^2}`

`\\ \tt\hookrightarrow \sigma=\sqrt{(125696)/(20)-(78.5)^2}`

`\\ \tt\hookrightarrow \sigma=√(6284.8-6162.25)`

`\\ \tt\hookrightarrow \sigma=√(122.55)`

`\\ \tt\hookrightarrow \sigma=11.07=11.1`

Way-2(Apply range-rule of thumb):-

• So the rule basically defines that range is approximately equal to four times of standard deviation.

`\\ \tt\hookrightarrow Range=max-min=100-60=40`

NOW

`\\ \tt\hookrightarrow \sigma \approx (Range)/(4)`

`\\ \tt\hookrightarrow \sigma\approx (40)/(4)`

`\\ \tt\hookrightarrow \sigma\approx 10`

• Make sure to use approx sign instead of equal to as range -rule of thumb doesn't give accurate standard deviation.

Answer 2

s=10

Explanation:

Basically, the range rule-of-thumb is that the range is generally about four times the standard deviation.

First, we find the range:

Range=Maximum-Minimum

Range=100-60

Range=40

Next, divide the range by 4 to get the standard deviation

Range=4(Standard Deviation)

40=4(Standard Deviation)

10=Standard Deviation

Therefore, s=10, which is the standard deviation