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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.
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