MEASURES OF CENTRAL TENDENCY

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Group Members:

Name: ID:

Rejvi Ahmed 13307132

Md. A.M. Tanvir 13307081

Mosaddiqur Rahman 13307094

Mazno Dewan 13307031

Mustafizur Rahman 13307048

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CONTENTS

What is Central Tendency?

Arithmetic Mean(AM) With Calculation

Median With Example

Mode With Example

Geometric Mean(GM) With Calculation

Harmonic Mean(HM) With Calculation

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Central Tendency

The central tendency is measured by averages. These describe the point about which the various observed values cluster

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set.

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Measures of Central Tendency

There are 5 Measures of central Tendency:

Arithmetic Mean(AM)

Median

Mode

Geometric Mean(GM)

Harmonic Mean(HM)

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Arithmetic Mean(AM)oThe arithmetic mean is the sum of a set of

observations, positive, negative or zero, divided by the number of observations.

o If we have “n” real numbers x1,x2,x3,………………xn

their arithmetic mean, denoted by , can be expressed as:

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Calculation of ARITHMETIC MEAN

Find the arithmetic Mean of 9,3,7,3,8,10,2

By using the formula of Arithmetic Mean We get,

So, The Arithmetic Mean = 6

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Median

The Median is the value that falls in the middle

when the observations are ordered into either ascending or descending numerical order.

If n is odd, The Median is the middle value

If n is even, The Median is the average of the two

middle values.

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How to Find The Median

To find the median, first the data set must be sort into either ascending or descending numerical order.

• Then, Select the median

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EXAMPLE of MEDIAN Find the Median from the data set:

3 , 12 , 4 , 6 , 1 , 4 , 2 , 5 , 8

After sorting from smallest to largest we get-

1, 2, 3, 4, 4, 5, 6, 8, 12

Now,

The Median is 4

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Mode

Mode is the value of a distribution for which the frequency is maximum. In other words, mode is the value of a variable, which occurs

with the highest frequency.

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Example of MODE

Find the mode of the data set :1, 2, 2, 3, 3, 3,

Here,

3 is the maximum times in the data set

So, The Median is 3.

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Example of MODE

Find the median from the data set: 1, 2, 2, 3, 3, 5

Here,

2 is two times and 3 is two times also

So, The data set has two modes 2 and 3.

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Geometric Mean(GM)

Geometric mean is defined as the positive root of the product of observations.

Symbolically,

GM=(x1*x2*x3*…………………….*xn)1/n

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Calculation of GEOMETRIC MEAN Find the Geometric Mean of 6,8,10,5,18

By using the formula of Geometric Mean We get,

GM=(6*8*10*5*18)1/5

=(43200)1/5

=8.454o This example will guide you to calculate the

harmonic mean manually

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Harmonic Mean(HM)

Harmonic mean is used to calculate the average of a set of numbers. Here the number of elements will be averaged and divided by the sum of the reciprocals of the elements. The Harmonic mean is always the lowest mean.

Harmonic Mean Formula : HM = N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN) Where, X = Individual score, N = Sample size (Number of

scores)

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Calculation of HARMONIC MEAN

To find the Harmonic Mean of 1,2,3,4,5

Step 1:Calculate the total number of values. N = 5 Step 2:Now find Harmonic Mean using the above formula. HM=N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)= 5/(1/1+1/2+1/3+1/4+1/5)= 5/(1+0.5+0.33+0.25+0.2)= 5/2.28So, Harmonic Mean = 2.19 This example will guide you to calculate the harmonic mean

manually

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QUESTION?

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THANK YOU

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