Find the median

[750+]

Can you please provide a solution?

[OptimusPrep]

Can you please provide a solution?

Median of a set with odd number of elements = the middle element of the set if arranged in ascending/descending order.
Median of a set with even number of elements = average of middle two numbers if arranged in ascending/descending order.

In the given case, total elements = 2 + 10 + 16 + 27 + 18 = 73 = 36 + 1 + 36
Hence the median will be the 37th term.
The 37th term will lie in the range 80 - 89

Correct Option: C

[Brent@GMATPrepNow]

50-59 2
60-69 10
70-79 16
80-89 27
90-99 18

The table above shows the distribution of test scores for a group of management trainees.
Which score interval contain the median of the 73 scores?

(a) 60-69
(b) 70-79
(c) 80-89
(d) 90-99
(e) It cannot be determined from the information given

Since we have an ODD number of values, the median will be the MIDDLEMOST value. In other words, if we arrange all 73 values in ASCENDING order, the median will be the 37th value (i.e., 36 values are below and 36 values are above).

The table says the first 2 scores in the 50-59 range. So, the 1st and 2nd values will be in the 50-59 range.
The table says the next 10 scores in the 60-69 range. So, 3rd to 12th values will be in the 60-69 range.
The table says the next 16 scores in the 70-79 range. So, the 13th to 28th values will be in the 70-79 range.
The table says the next 27 scores in the 80-89 range. So, the 29th to 45th values will be in the 80-89 range.

As we can see, the 37th value must be in the 80-89 range.

Answer: C

Cheers,
Brent