Transcript Measures of Variability (Dispersion)

Measures of Variability
(Dispersion)
Measures of Variability

Range
– Range = (High Score - Low Score+1)
– Summary of Range
 Least
stable-based on only two scores in distribution
 Can’t compare across distributions of different
sample sizes.
 With small samples, about as good as any measure.
– .e.g... Used in quality control
 Range
is used with mode.
Measures of Variability
Range
 Semi-Interquartile Range

– Defines a range on either side of the Mdn.
which contains the middle 50% of the scores
Measures of Variability

Semi-Interquartile Range
Q
Q Q
3
1
2
Of course to
actually do this,
we have to
know how to
calculate Q3 &
Q1
Measures of Variability

Semi-Interquartile Range
– Q2 and the Mdn. are the same
thing.
– Q1 Point on scale above which
75% of the scores fall and below
which 25% fall.
– Q3 Point on scale above which
25% of the scores fall and below
which 75% fall.
Now lets
get down to
how we do
these
calculations
.
Measures of Variability

Semi-Interquartile Range
– Q2 is the median, and we calculate the other
quartiles just like the median, but we use n/4
instead of n/2.
Measures of Variability

Semi-Interquartile Range
115.75  90
Q
 12.875
2
•The middle 50% of of scores fall between:
91.005 - 116.755
Measures of Variability

Semi-Interquartile Range
– Summary
 Mdn.
is used with Q
 Mdn.  Q defines range including middle 50% of
scores.
 Q is more stable since it isn’t influenced by extreme
scores like the range.
Measures of Variability



Range
Semi-Interquartile Range
Average Deviation
–
–
–
–
Computed by averaging the deviation of each score from the mean.
Problem is, sum is always zero so average is not possible.
This is solved by using absolute values
The problem with this is that the result can only be used for
description and is not useful for any subsequent calculations.
– Is used with the Mean -  1AD marks a range including 58% of the scores.
Measures of Variability



Range
Semi-Interquartile Range
Average Deviation
N
AD 
x
1
N
k
AD 
x  (X  X)
fx
1
N
mp
Measures of Variability




Range
Semi-Interquartile Range
Average Deviation
Standard Deviation s
Measures of Variability
Standard Deviation s
Raw (Ungrouped) data
N
s
x
1
N
N
x
2
OR s =
  X  X
2
1
N 1
Measures of Variability
Standard Deviation s
Raw (Ungrouped) data
Next we will see how to compute the standard deviation.
You will see that there are lots of ways to calculate this
important statistic - they all yield an important descriptive
statistic - THE STANDARD DEVIATION
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