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The chart above represents the number of students at five schools, eac 12 Jan 2017, 00:10
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The chart above represents the number of students at five schools, each of which has branches in each of four towns. In which town is the standard deviation of the number of students at each school the least?

A. Town A
B. Town B
C. Town C
D. Town D
E. Cannot be determined.

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C
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The chart above represents the number of students at five schools, eac 12 Mar 2017, 20:33
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Bunuel
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The chart above represents the number of students at five schools, each of which has branches in each of four towns. In which town is the standard deviation of the number of students at each school the least?

A. Town A
B. Town B
C. Town C
D. Town D
E. Cannot be determined.

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2017-01-12_1108.png

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Town having least deviation from its mean position has the least SD

Town A= 217-95 = 122
Town B=156-99 =57
Town C= 204-148 =56
Town D=220-35 = 185

Since town C has less deviation it has least SD

Ans C
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The chart above represents the number of students at five schools, eac 12 Mar 2017, 21:56
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Standard Deviation is the dispersion of elements from the mean position .
In Town C dispersion is the lowest i.e Maximum element- minimum element =204-148 =56
Hence Answer is C
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The chart above represents the number of students at five schools, eac 19 Jan 2026, 07:46
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I don't think the above replies are wholly accurate... I don't think the smallest outlier value guarantees the smallest standard deviation?? Isn't it based on the entire data spread?

Standard deviation is the square root of the average of the squared differences between each set element and the set mean. Good luck calculating that in your head - I can't!

But by recognizing that the RANGE of Town C (maximum - minimum) is significantly less than the other towns and that the elements are fairly clustered around a central value of 160-ish, I was confident in intuiting that Town C would have the smallest standard deviation.

Is my logic correct or am I missing a hidden math rule of thumb here?
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The chart above represents the number of students at five schools, eac 19 Jan 2026, 08:53
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AndyRugger, I believe your logic is correct, but rather than using intuition, it's better to check with formulae.

Since calculating the standard deviation is very time-consuming, before replying to the query, I personally solved it with both approaches.

Approximately Range=4 times SD, and using this relation, we can arrive at the conclusion that option C is correct.

Hope it helps
AndyRugger
I don't think the above replies are wholly accurate... I don't think the smallest outlier value guarantees the smallest standard deviation?? Isn't it based on the entire data spread?

Standard deviation is the square root of the average of the squared differences between each set element and the set mean. Good luck calculating that in your head - I can't!

But by recognizing that the RANGE of Town C (maximum - minimum) is significantly less than the other towns and that the elements are fairly clustered around a central value of 160-ish, I was confident in intuiting that Town C would have the smallest standard deviation.

Is my logic correct or am I missing a hidden math rule of thumb here?
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The chart above represents the number of students at five schools, eac 19 Jan 2026, 09:13
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AbhishekP220108
AndyRugger, I believe your logic is correct, but rather than using intuition, it's better to check with formulae.

Since calculating the standard deviation is very time-consuming, before replying to the query, I personally solved it with both approaches.

Approximately Range=4 times SD, and using this relation, we can arrive at the conclusion that option C is correct.

Hope it helps
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I appreciate the insight! I believe, however, that the Range/4 = approx. Standard Deviation is based on the normal distribution curve, which isn't a wholly accurate assumption with these sample sets. It'll get you close, though. In this case, the range was different enough that the rule of thumb worked, but it's only an approximation for real data sets, not an equality.
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