Measures of Dispersion

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Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

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Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
By:By:
Community Medicine Deptt:Community Medicine Deptt: BILAWAL MEDICAL COLLEGEBILAWAL MEDICAL COLLEGE
(LUMHS)(LUMHS) Jamshoro, Sind,Jamshoro, Sind, PakistanPakistan
e maile mail mnajeeb80@gmail.commnajeeb80@gmail.com
LIAQUAT
MEDICAL
UNIVERSITY

3. MEASURES OF DISPERSION
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4. MEASURES OF DISPERSION
1- Range.
2- Mean deviation (M.D.)
3- Variance.
4- Standard deviation (S.D.)
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5. Measures of DispersionMeasures of Dispersion
OR (spread or range of variability)
 Measures of dispersion: refers to the
spread of values about the mean.
 Basic question: how much do values differ for
a variable from the min to max, and distance
among scores in between. We use:
 Range (difference between the greatest and the least number in the data.)
 Mean Deviation (average of the deviations from the arithmetic mean)
 Variance (The average of the squared differences from the Mean)
 Standard Deviation (square root of Variance)

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7.  Remember that we said in order to
clean information from data, i.e. to
make an inference, we need to see
variability in our variables.
 Measures of dispersion give us
information about how much our
variables vary from the mean,
because if they don’t it makes it
difficult infer anything from the
data. Dispersion is also known as
the spread or range of variability.

8. RANGE
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What is the range?
 The range is the difference between
the greatest and the least number in
the data.
2, 4, 6, 8
Least No: Greatest No:
8 – 2 = 6. The range is 6.

10. Mean deviation
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11. Mean deviation
 Definition:
It is the average of the deviations from the
arithmetic mean.
 Formula:
M.D = ───────────
η
2
Mean Dev:
Data
X
Arithmetic
Mean
Dev from
Mean -
(X-X)
2 -5 -3
4 -5 -1
6 -5 1
8 -5 3
20/4 8/4
Mean 5 2

12. Variance
Data
X
Arithmeti
c Mean
-
X
Dev from
Mean -
(X-X)
Squared
differen
ces
2 -5 -3 (3)2
=9
4 -5 -1 (1)2
=1
6 -5 1 (1)2
=1
8 -5 3 (3)2
=9
20/4 8/4 20/n-1
Mean 5 Mean
Dev: 2
20 /3
“The average of the squared differences from the mean,”
Steps
Calculate the Mean
Subtract Mean from data
Square each result
Add squared result
Divide by n-1
Def:
The sum of the squares of
the deviation of each
measurement in a series from the
mean of the series divided by n-1
= (X-X)2 = squared deviation of mean
n-1 n-1
6.6
6.6
BUT:BUT: standard deviation is thestandard deviation is the square root of the variancesquare root of the variance √6.6 = 2.5

13. SStandard deviation (S.D)tandard deviation (S.D)
 SStandard deviation is thetandard deviation is the
square root of the variancesquare root of the variance
√6.6 = 2.5
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Variance and Standard DeviationVariance and Standard Deviation
• TheThe variancevariance && standard deviationstandard deviation
are the most common andare the most common and usefuluseful
measures of variabilitymeasures of variability..
•These two measures provideThese two measures provide
information aboutinformation about how the data varyhow the data vary
about the meanabout the mean..

15. NORMAL DISTRIBUTION CURVE
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/ Gaussian Curve
Mean, Median & Mode are
equal to one another
50% values above Meam
50% values below Meam
Tails come closer to axis
but never touch it

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Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

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