AnimeBrainly
Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

[tex]n = 20[/tex] , ∑[tex]x = 1570[/tex] , ∑[tex]x^2 = 125696[/tex] , 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).

Sagot :

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.

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

Mean:-

[tex]\\ \tt\hookrightarrow \overline{x}=\dfrac{\sum x}{n}=\dfrac{1570}{20}=78.5[/tex]

Standard deviation:-

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

WAY-1(apply common formula)

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

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

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{6284.8-6162.25}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=\sqrt{122.55}[/tex]

[tex]\\ \tt\hookrightarrow \sigma=11.07=11.1[/tex]

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

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

[tex]\\ \tt\hookrightarrow Range=max-min=100-60=40[/tex]

NOW

[tex]\\ \tt\hookrightarrow \sigma \approx \dfrac{Range}{4}[/tex]

[tex]\\ \tt\hookrightarrow \sigma\approx \dfrac{40}{4}[/tex]

[tex]\\ \tt\hookrightarrow \sigma\approx 10[/tex]

  • Make sure to use approx sign instead of equal to as range -rule of thumb doesn't give accurate standard deviation.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.