How to figure the raw score above and below

Question

If a researcher wishes to study only the middle 50% of the population, above and below which raw scores should she exclude potential subjects? Means=100 sd=15

Answer 1

We begin with what is provided.  We know that they want to study the middle 50% thus our two points of focus are the raw values at 25% and 75%.

 

Since we are working with normal distribution,  ( I am assuming since not stated otherwise) we need to find a way to reverse engineer the percentages into raw data.  

 

The method of converting data to a percentage when given the mean and standard deviation is to establish a z score and reference our table to finf our percentage.

 

In this case we do the opposite,  we find the closest table listings matching 25% and 75%.

 

Upon reference we find 25% = -.607 and 75% = .607

 

From here its all algebra. 

 

Remember we find out Z score by: (X - MEAN)/SD = Z

 

thus:

 

.607 = (X-100)/15

24.7117 = X-100

X = 124.7117 FOR 75%

 

AND

 

-.607 = (X-100)/15

-24.7117 = X-100

X = 75.2883 FOR 25%

 

These two numbers representing the two raw data points at which exclusion should begin to study only the middle 50%.

 

I hope this helps.