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MEASURES OF DISPERSION

Measures of Dispersion
➢ In statistics, to describe the data set accurately, statisticians must know more than
the measures of central tendency
...

➢ An average taken by itself may not always be very meaningful
...


❖ The measure of dispersion helps us to study the variability of the items
...

❖ The commonly used measures of dispersion are :
✓ Range
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✓ Mean deviation
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✓ Variance
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The symbol R is used for the
range
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Bluman”
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▪ The symbol for the population variance is 𝜎 2 (𝜎 is the Greek
lowercase letter sigma)
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All the text, examples, diagrams are taken from “Elementary Statistics, 10th ed, Allan G
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Measure of Variation for ungrouped data

Standard Deviation:
• The standard deviation is the square root of the variance
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• The corresponding formula for the standard deviation is
 =

2
(
x
−
x
)
 i

n

All the text, examples, diagrams are taken from “Elementary Statistics, 10th ed, Allan G
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Measure of Variation for ungrouped data

Example for Variance and Standard Deviation
Metabolic rates of 7 men (cal
...
) :
1792 1666 1362 1614 1460 1867 1439

STEP 1:
1792 + 1666 + 1362 + 1614 + 1460 + 1867 + 1439
11,200
𝑥ҧ =
=
7
7
𝑥ҧ = 1600

Example for Variance and Standard Deviation

Observations

Squared deviations

𝒙𝒊

Deviations
ഥ
𝒙𝒊 - 𝒙

1792

1792−1600 = 192

(192)2 = 36,864

1666

1666 −1600 =

1362

1362 −1600 = -238

1614

1614 −1600 =

1460

1460 −1600 = -140

1867

1867 −1600 = 267

(267)2 = 71,289

1439

1439 −1600 = -161

(-161)2 = 25,921

sum =

0

ഥ)𝟐
(𝒙𝒊 − 𝒙
66
14

(66)2 =

(-140)2

𝟐𝟏𝟒, 𝟖𝟕𝟎
𝟕

𝑽𝒂𝒓 = 𝐒𝟐 = 30695
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𝟕𝟏𝟒
𝐒
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Coefficient of Variation = Relative Dispersion x 100%
It is generally expressed in percentage
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The mean life times of both tubes
are 1375 and 1525 hours respectively, with standard deviations
of 280 and 345 hours respectively
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2036
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2196
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