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Standard deviation of the numbers 9, 9, 10, 11, 11
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09 Oct 2024, 23:14
09 Oct 2024, 23:14
Expert Reply
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Question Stats:
87% (00:21) correct
12% (01:10) wrong based on 8 sessions
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Quantity A |
Quantity B |
Standard deviation of the numbers 9, 9, 10, 11, 11 |
Standard deviation of the numbers 6, 8, 10, 12, 14 |
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Standard deviation of the numbers 9, 9, 10, 11, 11
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14 Dec 2024, 10:38
14 Dec 2024, 10:38
Expert Reply
The two sets are $\(\{9,9,10,11,11\} \&\{6,8,10,12,14\}\)$
The arithmetic mean (average) of the two sets is $\(=\frac{9+9+10+11+11}{5}=\frac{50}{5}=10 \quad\)$ \& $\(=\frac{6+8+10+12+14}{5}=\frac{50}{5}=10\)$ respectively. $\(\frac{Arithmetic Mean }{ Average }= \frac{Sum of terms }{Number of terms} \)$
The values of the second set i.e. $\(\{6,8,10,12,14\}\)$ are more dispersed $\((Gaps- $-4,-2,0,2,4\}\)$ from the mean when compared with the values of the first set i.e. $\(\{9,9,10,11,11\}\)$ which has a gap of $\(\{-1,-1,0,1,1\}\)$.
Hence the standard deviation of set $\(B\)$ would be higher when compared with set $\(A\)$, so the answer is (B).
The arithmetic mean (average) of the two sets is $\(=\frac{9+9+10+11+11}{5}=\frac{50}{5}=10 \quad\)$ \& $\(=\frac{6+8+10+12+14}{5}=\frac{50}{5}=10\)$ respectively. $\(\frac{Arithmetic Mean }{ Average }= \frac{Sum of terms }{Number of terms} \)$
The values of the second set i.e. $\(\{6,8,10,12,14\}\)$ are more dispersed $\((Gaps- $-4,-2,0,2,4\}\)$ from the mean when compared with the values of the first set i.e. $\(\{9,9,10,11,11\}\)$ which has a gap of $\(\{-1,-1,0,1,1\}\)$.
Hence the standard deviation of set $\(B\)$ would be higher when compared with set $\(A\)$, so the answer is (B).
gmatclubot
Standard deviation of the numbers 9, 9, 10, 11, 11 [#permalink]
14 Dec 2024, 10:38
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