Problem Solving

Table:

Score Interval----- Number of scores
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 contains 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.

How do I solve this?

Thanks!

SharonRaj wrote:Table:

Score Interval----- Number of scores
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 contains 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.

How do I solve this?

Thanks!

The correct answer is C
This is by no means the "proper" algebraic approach, but here's what I do in these types of questions:
1. I give the different ranges a variable. Lets say:
50-59 = A
60-69 = B
70-79 = C
80-89 = D
90-99 = E
2. Now we know there are 2 A's 10 B's 16 C's 27 D's and 18 E's, and we know the median is the middle variable in the set.
3. So, list them all out like this:
AABBBBBBBBBBCCCC..... EEEEE. It's a little tedious, but I like the visualization.
4. Then cancel out one value at a time from both sides.
5. Finally you will find a middle variable, here it is D. What is D? D=80-89. So the correct answer is C.

Let me know if this helps

Hi,

My approach is to find the median from 73 sample scores.

So, the median is (73+1)/2 = 37.

Then, you add the number of score from the lowest tier. From tier 50-59 to 70-79, you will get 28 scores (2+10+16).

Now you know that the median at 37 is contained in the tier 80-89 since 28+27 = 55 scores which already higher than 37.

Answer is C.

alex.gellatly: Thanks! That was helpful and easy to understand but a little time consuming

Trojanas: Thanks to you too. You mentioned the median is 37 and it is in tier 70-79 but the answer is C (80-89). At first, I was a bit confused but I guessed it was a typing error:)

trojanas wrote:Hi,

My approach is to find the median from 73 sample scores.

So, the median is (73+1)/2 = 37.

Then, you add the number of score from the lowest tier. From tier 50-59 to 70-79, you will get 28 scores (2+10+16).

Now you know that the median at 37 is contained in the tier 70-79 since 28+27 = 55 scores which already higher than 37.

Answer is C.

Thanks, SharonRaj!! You are right, I already corrected it.

SharonRaj wrote:Trojanas: Thanks to you too. You mentioned the median is 37 and it is in tier 70-79 but the answer is C (80-89). At first, I was a bit confused but I guessed it was a typing error:)

trojanas wrote:Hi,

My approach is to find the median from 73 sample scores.

So, the median is (73+1)/2 = 37.

Then, you add the number of score from the lowest tier. From tier 50-59 to 70-79, you will get 28 scores (2+10+16).

Now you know that the median at 37 is contained in the tier 70-79 since 28+27 = 55 scores which already higher than 37.

Answer is C.