Trying to fit normal dist. to quartile data

#1
I have taken a test to get into graduate school and have scored a 160.

The range of scores is 120 to 180.

The school I have applied to has 25th, 50th, and 75th scores of its applicants published as 149, 150, and 152 respectively. There are 49 applicants.

Is it possible to assume a normal distribution of scores and fit it to my quartile data? I'm trying to determine what percentile the 160 score is.
 

JohnM

TS Contributor
#2
You are free to assume anything.....whether or not the assumption is valid is unknown unless you have a list of all the scores....:D

Using a bell-shaped curve, and assuming the mean and median are the same, then the mean would be around 150. You can estimate the std dev from the fact that the 75th percentile is 152.

The 75th percentile corresponds to a z score of 0.674. Using the formula:

z = (x - mu)/s

0.674 = (152 - 150)/s

s = 2/0.674 = 2.967

Now, using your score of 160:

z = (160-152)/2.967
z = 2.696
which corresponds to the 99.6 percentile
 
#3
Thanks for the help. What could I look up in my old statistics book to follow what you did? I looked up normal distribution, but it didn't really have anything about extrapolating from the quartiles. It's been awhile.
 

JohnM

TS Contributor
#4
You won't find discussion of a direct relationship between the normal distribution and quartiles, but if you read under how to use the normal tables (z tables) to find areas under the curve, that should remove some of the rust.