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Each of 5 households owns at least one television set. What is the sta

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Bunuel
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Each of 5 households owns at least one television set. What is the sta [#permalink] New post   15 Sep 2020, 07:00
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Each of 5 households owns at least one television set. What is the standard deviation of the numbers of television sets owned by the 5 households?

(1) At least 4 of the households own the same number of television sets.

(2) One of the households owns 3 television sets.
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Re: Each of 5 households owns at least one television set. What is the sta [#permalink] New post   15 Sep 2020, 07:14
Each of 5 households owns at least one television set. What is the standard deviation of the numbers of television sets owned by the 5 households?

(1) At least 4 of the households own the same number of television sets.

(2) One of the households owns 3 television sets.

Explanation:
S1: there will be two cases

Case1-Out of Five either 4 own same no. Of TV sets(insufficient)

Case2-all 5 own same no. Of TV sets(sufficient as mean= each value & S.D=0)

As both cases possible hence S1 is insufficient

S2:One of the households owns 3 television sets.
Not possible to tell S.D as information about each household not available.

Combining both S1& S2
Again two cases will exist same as in S1

Hence E is the correct answer.

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Atul Pandey

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Re: Each of 5 households owns at least one television set. What is the sta [#permalink] New post   01 Oct 2020, 08:30
I think the answer should be E.

1 - We don't know the exact number of TV sets for 4 households and the number of TV sets owned by the remaining household. Also, note that the option says at least 4 households which means that it is possible that all 5 households own the same number of TV sets and in this case the SD will be 0.

2 - Not sufficient.

1+2 - We now know that SD cannot be 0 but we still don't know the number of TV sets owned by 4 households, so not sufficient again.

Bunuel wrote:
Each of 5 households owns at least one television set. What is the standard deviation of the numbers of television sets owned by the 5 households?

(1) At least 4 of the households own the same number of television sets.

(2) One of the households owns 3 television sets.
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Re: Each of 5 households owns at least one television set. What is the sta [#permalink] New post   23 Dec 2020, 06:36
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Bunuel wrote:
Each of 5 households owns at least one television set. What is the standard deviation of the numbers of television sets owned by the 5 households?

(1) At least 4 of the households own the same number of television sets.

(2) One of the households owns 3 television sets.


\(The \ distance \ among \ the \ numbers \ is \ the \ standard \ deviation. \)

(1) We don't know other one's value. For magnitude changes in the value of the other person, the standard deviation will change. We will not get any specific value; Insufficient.

(2) We don't know the rest of the fours' value. Insufficient.

Considering both: One household may have 3, other four may have any equal value.

The four households may have 3 one household may have any value. Insufficient.

The answer is \(E.\)
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Re: Each of 5 households owns at least one television set. What is the sta [#permalink] New post   19 Jan 2023, 03:46
Hello from the GMAT Club BumpBot!

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Re: Each of 5 households owns at least one television set. What is the sta [#permalink]
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