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Which of the following is correct about the data described by the box-
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16 Jan 2024, 03:16

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Which of the following is correct about the data described by the box-and-whisker plot above?

Indicate all such statements.

(A) The median of the whole set is closer to the median of the lower half of the data than it is to the median of the upper half of the data.

(B) The set has a standard deviation greater than zero.

(C) The mean of the whole set is greater than the median.

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Re: Which of the following is correct about the data described by the box-
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30 Mar 2024, 14:15

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OFFICIAL EXPLANATION

A box-and-whisker plot is a convenient means of graphically representing data using quartiles. We have three major points: the first middle point (the median, or Q2), and the middle points of the two halves, the lower quartile (Q1) and the upper quartile (Q3), which divide the entire data set into quarters, called ‘quartiles’. Q1 is the middle number for the first half of the list, Q2 is the middle number for the whole list, and Q3 is the middle number for the second half of the list. The box in the middle, i.e. from Q1 to Q3 represents the middle 50 percent of the data, also known as the Inter-Quartile-Range (Q3 − Q1).

Thus, the box is used to identify each of the two middle quartile groups of data, and the ‘whiskers’ extend outward from the boxes to the lowest and highest values observed.

Option A:

Median of the whole set = Q2

Median of the lower half of the data = Q1

Median of the upper half of the data = Q3

We can observe that, in the given box-and-whisker plot, Q2 is closer to Q1 than to Q3.

Thus, the median of the whole set is closer to the median of the lower half of the data than it is to the median of the upper half of the data. – Correct

Option B:

Standard deviation is ‘0’ only for data which has the same value, i.e. no spread. The box-and-whisker plot above clearly shows the spread of the data. Hence, the standard deviation must be greater than zero. – Correct

Option C:

In a box-and-whisker plot, no information can be derived about the mean. Thus, the mean need not be mid-way of the box. Thus, we cannot determine whether the mean of the whole set is greater than the median. – Incorrect

The correct answers are options A and B.

_________________

A box-and-whisker plot is a convenient means of graphically representing data using quartiles. We have three major points: the first middle point (the median, or Q2), and the middle points of the two halves, the lower quartile (Q1) and the upper quartile (Q3), which divide the entire data set into quarters, called ‘quartiles’. Q1 is the middle number for the first half of the list, Q2 is the middle number for the whole list, and Q3 is the middle number for the second half of the list. The box in the middle, i.e. from Q1 to Q3 represents the middle 50 percent of the data, also known as the Inter-Quartile-Range (Q3 − Q1).

Thus, the box is used to identify each of the two middle quartile groups of data, and the ‘whiskers’ extend outward from the boxes to the lowest and highest values observed.

Option A:

Median of the whole set = Q2

Median of the lower half of the data = Q1

Median of the upper half of the data = Q3

We can observe that, in the given box-and-whisker plot, Q2 is closer to Q1 than to Q3.

Thus, the median of the whole set is closer to the median of the lower half of the data than it is to the median of the upper half of the data. – Correct

Option B:

Standard deviation is ‘0’ only for data which has the same value, i.e. no spread. The box-and-whisker plot above clearly shows the spread of the data. Hence, the standard deviation must be greater than zero. – Correct

Option C:

In a box-and-whisker plot, no information can be derived about the mean. Thus, the mean need not be mid-way of the box. Thus, we cannot determine whether the mean of the whole set is greater than the median. – Incorrect

The correct answers are options A and B.

_________________

gmatclubot

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