Question

Given a set of data sorted from smallest to largest, define the first, second, and third quartiles.

a. The first quartile is the area within one standard deviation of the mean.
The second quartile is the area within two standard deviations of the mean.
The third quartile is the area within three standard deviations of the mean.
b. The first quartile is the mean of the lower half of the data below the median.
The second quartile is the median
The third quartile is the mean of the upper half of the data above the median.
c. The first quartile is the minimum value.
The second quartile is the median.
The third quartile is the maximum value.
d. The first quartile is the median of the lower half of the data below the overall median.
The second quartile is the overall median
The third quartile is the median of the upper half of the data above the overall median.
e. The first quartile is the area that contains the 25% of all values that are closest to the mean.
The second quartile is the area that contains the 50% of all values that are closest to the mean.
The third quartile is the area that contains the 75% of all values that are closest to the mean.

Answer 1

Explanation:

Given a set of data sorted from smallest to largest, i.e. arranged in ascending order we are to find out the median, I and III quartiles

We know that the median is the middle entry of data arranged in ascending order

Q1 is the entry below which 25% lie and Q3 is one above which 25% lie

Hence proper definition would be

d. The first quartile is the median of the lower half of the data below the overall median.

The second quartile is the overall median

The third quartile is the median of the upper half of the data above the overall median.

Option b is wrong becuase mean is not necessary here. Option a is wrong because this has nothing to do with std deviation

Option c is wrong since minimum value cannot be q1

Option e is wrong because we have exactly 25% lie below Q1