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8/10/2019 UnitI Measures of Central Tendency
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Definition
Objectives
Properties
PrerequisitesMerits and Demerits
Mean
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Copyright 2000 by Monica Yuskaitis
Definition
Mean is an attempt to find one single
figure to describe whole of figures -
Clark
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Copyright 2000 by Monica Yuskaitis
Objectives
To get single value that describes thecharacteristic of entire group
To facilitate comparison measures ofcentral value
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Copyright 2000 by Monica Yuskaitis
Properties
1. The sum of the deviations of the item fromthe arithmetic mean is always zero.
i.e., (X-X) = 0
2. The Sum of the squired deviations of theitems from the arithmetic mean is minimum.
i.e., (X-any value) > (X-X)
2
22
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Copyright 2000 by Monica Yuskaitis
3. If we replace each item in the series by the mean,
then sum of these substitutions will be equal to the
sum of the individual items
i.e., If X=150 and N = 5 then
30+30+30+30+30 =150
Combined arithmetic mean can be computed by
(N X + N X )/(N + N )11 122 2
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Copyright 2000 by Monica Yuskaitis
Requisites of a Good Average
Easy to Understand
Simple to compute
Based all ItemsNot be unduly affected by extreme
values
Rigidly defined
Capable of further algebraic
treatments
Sampling Stability
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Copyright 2000 by Monica Yuskaitis
Merits
Simplest and Easiest to compute
Affected by the value of every item
Rigid Mathematical Formula
Subsequent algebraic treatment
Balancing the values
Not based on position
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Copyright 2000 by Monica Yuskaitis
Demerits
Can not be calculated for an openend classes
Not a good measure just a characteristic
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Copyright 2000 by Monica Yuskaitis
Objectives
To get single value that describes thecharacteristic of entire group
To facilitate comparison measures ofcentral value
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Copyright 2000 by Monica Yuskaitis
Properties1. The median for any set of data divides it into two
equal halves. One half consists of observationssmaller than the median. Observations in theother half are larger than the median.
2. The Sum of the absolute deviations of the itemsfrom the median is minimum.
i.e., (X-any value) > (X-Md)
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Copyright 2000 by Monica Yuskaitis
4. Median is determined by the position orlocation of observations in the array, andnot by their size or magnitude.
5. Median is not affected by the extremevalues in the data.
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Copyright 2000 by Monica Yuskaitis
Merits
1. Simplest and Easiest to compute
2. Useful in case of open ended distribution
3. Not influenced by extreme values
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Copyright 2000 by Monica Yuskaitis
Demerits
1. Since median is a positional average, its value isnot determined by each and every observation.
2. Not capable for further algebraic treatment.
3. Not a good measure just a characteristic
4. Less reliable average for estimation purposes.
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Copyright 2000 by Monica Yuskaitis
Demerits
5. Median tends to be rather unstable value if
the number of observations are small.
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Definition
Objectives
Properties
Merits and Demerits
Mode
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Copyright 2000 by Monica Yuskaitis
Objectives
To get single value that describes thecharacteristic of entire group
To facilitate comparison measures ofcentral value
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Copyright 2000 by Monica Yuskaitis
Merits
1. Simplest and Easiest to compute
2. Useful in case of open ended distribution
3. Not influenced by extreme values
4. Useful in case of qualitative data.
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Copyright 2000 by Monica Yuskaitis
De-Merits
1.Not Rigidly defined measure
2. Values cannot be computed in case of bi-
modal distribution
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