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fenix001 [56]
2 years ago
12

ula"> , ∑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).
Mathematics
2 answers:
devlian [24]2 years ago
6 0

Answer:

s=10

Step-by-step explanation:

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

<u>First, we find the range:</u>

Range=Maximum-Minimum

Range=100-60

Range=40

<u>Next, divide the range by 4 to get the standard deviation</u>

Range=4(Standard Deviation)

40=4(Standard Deviation)

10=Standard Deviation

Therefore, s=10, which is the standard deviation

zhenek [66]2 years ago
4 0

Mean:-

\\ \tt\hookrightarrow \overline{x}=\dfrac{\sum x}{n}=\dfrac{1570}{20}=78.5

Standard deviation:-

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

WAY-1(apply common formula)

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

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

\\ \tt\hookrightarrow \sigma=\sqrt{6284.8-6162.25}

\\ \tt\hookrightarrow \sigma=\sqrt{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 \dfrac{Range}{4}

\\ \tt\hookrightarrow \sigma\approx \dfrac{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.
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