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Re: In the distribution of the variable A, the mean is 56.... [#permalink]
Can someone please help with this question?
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In the distribution of the variable A, the mean is 56.... [#permalink]
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bunterocks wrote:
In the distribution of the variable A, the mean is 56 and the measurement p lies between the 65th and 70th percentiles. In the distribution of measurements of variable B, the mean is 56 and the measurement q lies between the 75th and 80th percentiles.

Quantity A
Quantity B
p
q


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


In a normal distribution - 65th, 70th, 75th, 80th percentiles all lie between mean and 1σ above mean.

Here, both the distributions A and B have a mean of 56, but, we have no idea about their standard deviation!
Let's take 2 cases here;

Case I:
\(σ_A = 10\)
\(σ_B = 2\)

Col. A: a value between 56 and 66
Col. B: a value between 56 and 58

So. Col. A > Col. B

Case II:
\(σ_A = 2\)
\(σ_B = 10\)

Col. A: a value between 56 and 58
Col. B: a value between 56 and 66

So. Col. A < Col. B

Hence, option D
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Re: In the distribution of the variable A, the mean is 56.... [#permalink]
KarunMendiratta wrote:
bunterocks wrote:
In the distribution of the variable A, the mean is 56 and the measurement p lies between the 65th and 70th percentiles. In the distribution of measurements of variable B, the mean is 56 and the measurement q lies between the 75th and 80th percentiles.

Quantity A
Quantity B
p
q


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


In a normal distribution - 65th, 70th, 75th, 80th percentiles all lie between mean and 1σ above mean.

Here, both the distributions A and B have a mean of 56, but, we have no idea about their standard deviation!
Let's take 2 cases here;

Case I:
\(σ_A = 10\)
\(σ_B = 2\)

Col. A: a value between 56 and 66
Col. B: a value between 56 and 58

So. Col. A > Col. B

Case II:
\(σ_A = 2\)
\(σ_B = 10\)

Col. A: a value between 56 and 58
Col. B: a value between 56 and 66

So. Col. A < Col. B

Hence, option D


Thanks a lot for the detailed explanation.
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Re: In the distribution of the variable A, the mean is 56.... [#permalink]
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Re: In the distribution of the variable A, the mean is 56.... [#permalink]
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