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26 Sep 2023, 05:45
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C
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In a certain class of \(n\) students, the average (arithmetic mean) weight of all students is \(50\) kg. A new student joins the class. Does the standard deviation of the weight of the students decrease after the new student joins in?
1) The weight of the new student is \(50\) kg
2) The weight of each student in the class is distinct.
1) The weight of the new student is \(50\) kg
2) The weight of each student in the class is distinct.
Similar Question: Link
26 Sep 2023, 08:26
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gmatophobia
The average of n weights is 50 kg. We can denote the standard deviation of those n weights by SD₁, and we can denote the standard deviation of the n + 1 weights by SD₂.
We need to answer the question:
Is SD₂ < SD₁ ?
Statement One Alone:
=> The weight of the new student is 50 kg.
If each student weighs 50 kg, then adding a new student who also weighs 50 kg won’t change the standard deviation, which would remain zero. In this case, the answer is No.
According to a rule, if we add an extra item to a data set consisting of items that are not all the same so that the extra item is equal to the average of the original data set, the standard deviation will decrease.
So, if the weights of the original n students are not all the same, then adding a 50 kg weight, which is equal to the average of the original data set of weights, will decrease the standard deviation of the weights. In this case, the answer is Yes.
Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
=> The weight of each student in the class is distinct.
If the extra weight is equal to 50 kg, which is the average of the original data set of not all equal weights, the standard deviation will decrease. In this case, the answer is Yes.
If the extra weight is very far from the average of the original data set (for example, {49, 50, 51} => {49, 50, 51, 500}), then the standard deviation will increase. In this case, the answer is No.
Statement two is not sufficient. Eliminate answer choice B.
Statements One and Two Together:
Since we know that the extra weight is equal to 50 kg, which is the average of the original data set of not all equal weights, the standard deviation will decrease. The answer is a definite Yes.
The two statements together are sufficient.
Answer: C
26 Oct 2025, 10:20
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