90.9k views
22 votes

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).

2 Answers

8 votes

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.
User JakeCowton
by
8.5k points
3 votes

Answer:

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

User Shicholas
by
7.7k points
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