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Quartiles
Quartiles are merely particular percentiles that divide
the data into quarters, namely:
Q1= 1st quartile = 25th percentile (P25)
Q2= 2nd quartile = 50th percentile
= median (P50)
Q3= 3rd quartile = 75th percentile (P75)
Quartile Example
Using the applicant (aptitude) data,
the first quartile is:
Rounded up Q1= 13th ordered value = 46
Similarly the third quartile is:
P
100
n • = (50)(.75) = 37.5 38 and Q3= 75
n • = (50)(.25) = 12.5
P
100
Interquartile Range
The interquartile range (IQR) is
essentially the middle 50% of the
data set
IQR = Q3-Q1
Using the applicant data, the IQR is:
IQR = 75 -46 = 29
Z-Scores
qZ-score determines the relative position of
any particular data value x and is based on
the mean and standard deviation of the
data set
qThe Z-score is expresses the number of
standard deviations the value x is from the
mean
qA negative Z-score implies that x is to the left
of the mean and a positive Z-score implies
that x is to the right of the mean
Z Score Equation
z=x-x
s
For a score of 83 from the aptitude data set,
z= = 1.22
83 -60.66
18.61
For a score of 35 from the aptitude data set,
z= = -1.36
35 -60.66
18.61
Standardizing Sample Data
The process of subtracting the mean and dividing
by the standard deviation is referred to as
standardizing the sample data.
The corresponding z-score is the standardized
score.
