UnitI Measures of Central Tendency

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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Objectives

To get single value that describes thecharacteristic of entire group

To facilitate comparison measures ofcentral value


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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

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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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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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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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Demerits

Can not be calculated for an openend classes

Not a good measure just a characteristic


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Objectives




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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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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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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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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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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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Objectives




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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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De-Merits

1.Not Rigidly defined measure

2. Values cannot be computed in case of bi-

modal distribution

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UnitI Measures of Central Tendency