Median of Scores Problem

[xs2infa]

The table shows the distribution of test scores for a group of trainees.

Score Interval Number of Score
50-59 2
60-69 19
70-79 16
80-89 27
90-99 18

Which score interval contains the median of 73 scores?

A. 50-59
B. 60-69
C. 70-79
D. 80-99
E. 90-99

[sanju09]

The table shows the distribution of test scores for a group of trainees.

Score Interval Number of Score
50-59 2
60-69 19
70-79 16
80-89 27
90-99 18

Which score interval contains the median of 73 scores?

A. 50-59
B. 60-69
C. 70-79
D. 80-99
E. 90-99

The median of 73 scores is the 37th score. Prepare the "Cumulative Frequency" column next to the column "Number of Scores" to find which score interval would cover the 37th score and that's the answer.

Score Interval/Number of Score/ Cumulative Frequency
50-59 /2 /2
60-69 /19 /21
70-79 /16 /37
80-89 /27 /64
90-99 /18 /82

Clearly, the score interval 70-79 includes the 37th score and hence that's the answer.

[spoiler]C[/spoiler]

[xs2infa]

Thanks Sanju.

[HeintzC2]

You're distribution shows 82 scores, however, you ask for the median of 73 scores. I believe you have a typo in this question, notably, I've seen this question with 19 as a 10 instead. This way, you have a distribution of 73 scores, and are trying to find the median of these 73 scores. You cannot find a median for a set of numbers different than the distribution given, as you don't know which scores are actually included in the group to find the median of.

With the corrected problem, the median is still the 37th score, but that results in the 80-89 interval, or choice D.

The table shows the distribution of test scores for a group of trainees.

Score Interval Number of Score
50-59 2
60-69 19
70-79 16
80-89 27
90-99 18

Which score interval contains the median of 73 scores?

A. 50-59
B. 60-69
C. 70-79
D. 80-99
E. 90-99

The median of 73 scores is the 37th score. Prepare the "Cumulative Frequency" column next to the column "Number of Scores" to find which score interval would cover the 37th score and that's the answer.

Score Interval/Number of Score/ Cumulative Frequency
50-59 /2 /2
60-69 /19 /21
70-79 /16 /37
80-89 /27 /64
90-99 /18 /82

Clearly, the score interval 70-79 includes the 37th score and hence that's the answer.

[spoiler]C[/spoiler]

[sanju09]

You're distribution shows 82 scores, however, you ask for the median of 73 scores. I believe you have a typo in this question, notably, I've seen this question with 19 as a 10 instead. This way, you have a distribution of 73 scores, and are trying to find the median of these 73 scores. You cannot find a median for a set of numbers different than the distribution given, as you don't know which scores are actually included in the group to find the median of.

With the corrected problem, the median is still the 37th score, but that results in the 80-89 interval, or choice D.

When data is presented in the ascending or descending intervals of classes, the median location of any section of this list can be found out without worrying for what's included and what's not.