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1. Presentation on Measures
of Central tendency and
Dispersion
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2. CENTRAL TENDENCY
• Middle point of distribution
• Middle point at which the distribution is in balance
• Why it is necessary?
• Central tendency gives us simple and brief
description of the main features of the whole
data.
• The measures of central tendency or averages
reduce the data to a single value which is highly
useful for making comparison.
• Eg. Marks obtained by a student in a class
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3. MEASURES OF CENTRAL TENDENCY
MEAN
CENTRAL
TENDENCY
MODE MEDIAN
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4. DISPERSION
• Spread of data in the distribution
• To find out how far the variable is spread out in a distribution
• Why it is necessary?
• To analyze variability and uncertainty
• Observations are nearer to center- dispersion/scatter/variation-
small
• Observations are farther to center- dispersion/scatter/variation-
high
Eg. Random Experiment conducted in physics for measuring the
error of an equipment.
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5. MEASURES OF DISPERSION
RANGE
STANDARD
DEVIATION
DISPERSION
VARIANCE
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6. SKEWNESS & KURTOSIS IN DISPERSION
• Distribution curves- symmetric or skewed
• Skewness- concentration of values on 1 side
• Mean<median<mode.
• Positively/Right skewed- tailing off towards right
• Negatively/Left skewed- tailing off towards left
• Kurtosis- peakedness, how sharp the curve is which in turn
determines how less the variations are.
• K>3 Leptokurtic; K=3Mesokurtic; K<3Platykurtic
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7. SKEWNESS
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8. KURTOSIS
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9. MEAN
• ARITHMETIC MEAN
• WEIGHTED MEAN
• GEOMETRIC MEAN
• Useful when unique value is required for decision making
• Disadvantageous when large set of data needs to be
analyzed
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10. MEDIAN & MODE
• Median- Middle most observation
• Grouped and ungrouped data
• Mode- the value that is most repeated in the dataset
• Disadvantages of both- not affected by extreme values.
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11. MEDIAN
• EXAMPLE
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12. MEASURES OF DISPERSION
• RANGE
• INTERFRACTILE RANGE
• INTERQUARTILE RANGE
• STANDARD DEVIATION
• VARIANCE
• COEFFICIENT OF VARIATION- Standard deviation as a percentage
of mean.
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13. Use of Standard Deviation
• Example:
• An IQ test- Normally distributed-with a mean of 100
and σ of 15.
• About what % of people have IQ scores
A)above 100; B)above 145 C) below 85.
• Answer:
• Use 68-95-99.7 rule.
• 68% of the area in the curve- in 1*σ range
• 95% of the area in the curve- in 2*σ range
• 99.7% of the area in the curve- in 3*σ range.
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14. BINOMIAL DISTRIBUTION
• Used to model the number of success
REQUIREMENTS
• ‘n’ repeated identical independent trials
• Only 2 outcomes (success/failure)
• P(success)= p
• P(failure)=q
• Provided p+q=1
• P(x) = The probability that there will be exactly ‘x’ successes in ‘n’
trials given by
• P(x)= (n!/(n-x)!x!) *p^x*q^(n-x)
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15. BINOMIAL DISTRIBUTION
Example:
• In an exam with multiple choice- 10 questions-5
choices (a,b,c,d,e)- what is the probability u get
exactly 4 questions correct just by guessing.
• Answer: 0.09~= 9%
P(S)=0.5=p, P(F)=0.8=q.
N=10; x=4;
• Use P(x) = The probability that there will be exactly ‘x’ successes
in ‘n’ trials given by
• P(x)= (n!/(n-x)!x!) *p^x*q^(n-x)
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