STATISTICS�IN �ECONOMICS

Presentation on

Arithmetic Mean

​

Prepared By

CHANDIGARH REGION

PGT

​

PREM JEET KUMAR BHATI

TOPIC �FOR �THE DAY

​

​

​

Arithmetic Mean

Objectives

The student will be able to:

* Find the meaning of arithmetic

mean.

* Find the application of formulas of arithmetic mean in different series.

* Students will able to make easy solutions of numerical practices of Arithmetic Mean.

​

����What is meant by Arithmetic Mean?��

​

​

The Arithmetic Mean is the Numerical Average of the data set

or a Series.

​

​

How do we find it ?

The mean is found by adding all the values in the Data Set/Series, then dividing the sum by the Number of values.

It is also known as Arithmetic Average.

Lets find MEAN score?

97

84

73

88

100

63

97

95

86

+

783

783

÷

9

The mean is 87

A trial example for you :-

• A JNV school where

there are…..

• 20 students in class 9^th,
• 25 students in class 10^th ,
• 15 students in class 11^th …..and
• 12 students in class 12^th .

Find the Mean or Average Number of students in this JNV school……..

HINT :-

We need to find ……….

​

• Total number of

students.

​

• Total number of

classes.

​

• Application of Formula.

Solution :-

• Total number of students = 72
• Total number of classes = 4
• Application of Formula =

Arithmetic Mean= Total Number Of Students

No of Classes

​

• Therefore , Mean = 72/4 = 18

​

​

​

​

Types Of Mean

Simple Arithmetic Mean

*All items of a series

are given equal importance.

​

Weighted Arithmetic Mean

*Different items of a series are

accorded different weights

in accordance with their

relative importance

Computation of Mean

Methods for Computation

Abbreviations � used in Computation of Mean

• X = The variable
• ∑ X = Summation of Variable X
• f = Frequency
• ∑f or N = Number of observation
• f x = Product of frequency and variable
• ∑f X = summation of f X
• m = mid value
• fm = product of frequency and mid value
• A = assumed mean
• d or d x = deviation from X variable (X-A)
• C & i = common factor & interval
• d’ or d’x = step deviation

​

Formulae � Used in Computation of Mean

STATISTICS�IN �ECONOMICS

Presentation on

Median

​

Prepared By

CHANDIGARH REGION

PGT

​

PREM JEET KUMAR BHATI

TOPIC �FOR �THE DAY

​

​

​

Median

Objectives

The student will be able to:

* Find the meaning of median.

* Find the application of formulas of median in different series.

* Students will able to make easy solutions of numerical practices of Median.

​

What is the MEDIAN?�

The MEDIAN is the number that is in the middle of a set of data.

​

Median is what divides the score in the distribution into two equal parts.

​

50% lies below the median value and 50% lies above the median value.

​

It is also known as the middle score or the 50^th percentile.

​

​

​

Median

​

Sounds like

MEDIUM

Think middle when you hear median.

​

​

Computation of Median

Median Of Ungrouped Data

• How do we find it?

​

. Arrange the Scores ( From the

lowest to highest or highest

to lowest)

Determine the middle most score in a

distribution if n is an odd number and get

the average of two middle most scores if n is

an even number.

​

​

97

84

73

88

100

63

97

95

86

The median is 88.

Half the numbers are

less than the median.

Half the numbers are

greater than the median.

��How do we find the MEDIAN �When two numbers are in the middle of series ?� N is even number.

​

1. Add the two middle most numbers.

​

2. Then divide by 2.

​

​

97

84

73

88

100

63

97

95

88 + 95 = 183

183

÷

2

The median is

91.5

Median of Grouped Data

Discrete series :-

steps for……

​

1. Arrange the data in ascending or descending order.

2. Compute Cumulative frequency.

3.Apply the formula and locate the median at the size of items , in whose cumulative frequency the value of (n+1) the item lies.

2 Formula :- m = size of ( n+1)th item

2

Example :-

Calculate median (m) :-

​

​

Solution :-

​

​

m= size of n+1th item

2 M= 49+1 = 50

2 2

size of 25^th item m=61

​

​

​

Median of Grouped Data

Continuous series :-

steps for……

1. Compute Cumulative frequency.

2. Obtain median group by applying formula (n) item.

2

3. Finally apply the formula 2^nd formula.

Formula :-

m = l1 + N/2 – c.f. × i

f

Example :-

​

Calculate median (m) :-

​

​

​

​

Lets do this.....

​

​

Computation of c.f.

​

​

​

​

Applying formula

M = size of (N/2) item [ N= 80 ]

M = 80/2 = 40^th item

40^th item is located in class interval of 140-160

Now,

​

​

l1 = 140 , n/2 = 40 , c.f. =30, i = 20 , f = 30

M = 140+ 80/2 - 30 × 20

3 0 m = 140+6.67=146.67

M = 146.67

Properties of Median

• It may not be an actual observation in the data series.

​

• It can be applied in ordinal level

​

• It is not affected by extreme values because median is a positive measure.

​

• It is an average of Position

Merits and Demerits of Median

Merits

• Simplicity
• Ideal average
• Graphical determination
• Practical application
• Representing middle value

• Not based upon all observations
• Inaccurate in case of large data
• Arrangement required
• Lack of algebraic treatment

Demerits

That is all in the part of Median

Thank you

STATISTICS�IN �ECONOMICS

Presentation on

Mode

​

Prepared By:

CHANDIGARH REGION

PGT

​

PREM JEET KUMAR BHATI

TOPIC FOR THE DAY

MODE

​

​

Hello Friends. I want to order shoes for my class students. But I don’t know what size?

​

​

Shall I order same size shoes for all students?

​

​

Can statistics help me in This?

​

Yes! Definitely, The Mode can help you in this decision.

​

Moooode?

What is Mode?

​

Mode is defined as the size of the variable or score which occurs most frequently..

​

Oooh!

I understood. First I will take all my students’ shoe No.

​

​

Here is the measurement.

​

​

Five is Most repeated shoe No. so Mode is 5.

​

Example: Find the mode from the frequency distribution.

Calculating mode from the frequency distribution (Discrete Series)

In the above frequency distribution table, 50 occur maximum times with highest frequency 20. So the Mode will be 50.

Calculating mode from the frequency distribution (Continuous Series)

Formula:

Example: Gives the details different age group workers in a company. Compute the value of mode.

In above example the highest frequency is 35 so model class is 30-40. So:

L   =  lower limit of modal class  = 30

f1  =  frequency of modal class  = 35

fo  =  frequency of class preceding the modal class.  = 20

f2  =  frequency of class higher than modal class  = 15

I =  size or width of class interval. = 10

OR 30 + 4.3 Or 34.43

So Mode = 34.43

By putting the values in the formula

Calculating mode from the frequency distribution (Continuous Series) Using Grouping Method: This method is used when highest frequencies are given more than once.

Grouping Process:

1. At first, values are arranged in ascending order and frequency against each item is properly written.

​

1. Grouping table consists of the variable column and other six columns for frequencies. It is not necessary that we should have six columns for frequencies. These numbers can be reduced to 5 or 4 as per requirement. Sometimes the class interval containing mode is determined by observation.

These frequency columns contain the following:

Column 1: It contains all the frequency values.

Column 2: We add frequencies in group of two values starting from first value of column 1.

Column 3: We add frequencies in group of two values starting from second value of column 1.

Column 4: We add frequencies in group of three values starting from first value of column 1.

Column 5: We add frequencies in group of three values starting from second value of column 1.

Column 6: We add frequencies in group of three values starting from third value of column 1.

Note: Highest value in all the columns are encircled or underlined, so the mode seems to change.

Example:  Compute the value of mode from the following data using Grouping Method.

Solution: Calculation of mode with grouping table:

Analysis Table

Solution:

Analysis table shows that the class interval 20-25 has been repeated all the six times ,so the mode lies in the class 20-25. Applying the formula we get:

In above example the highest frequency is 35 so model class is 30-40. So:

L   =  lower limit of modal class  = 30

f1  =  frequency of modal class  = 35

fo  =  frequency of class preceding the modal class.  = 20

f2  =  frequency of class higher than modal class  = 15

I =  size or width of class interval. = 10

OR 20 + 3.46 Or 23.46

​

So Mode = 23.46

STATISTICS�IN �ECONOMICS

Presentation on

Partition values

​

Prepared By

CHANDIGARH REGION

PGT

​

PREM JEET KUMAR BHATI

TOPIC �FOR �THE DAY

​

​

​

Partition Values

Objectives

The student will be able to:

* Find the meaning of Partition

values.

* Find the application of formulas of

partition values in different series.

* Students will able to make easy solutions of numerical practices of Partition Values.

​

Partition Values

Partition values are

the values of a series

which divide the

data into a number

of equal points.

Some Partition Values are

• Median ,
• Quartiles ,
• Deciles ,
• Percentiles etc.

​

Median :-

Median is a location value .

It also act as a partition

value, for it divides the

total frequency

into two equal parts

Quartile :-

• It is the Quarter Value of the series.

​

• Quartiles are those values of the variables , which divides the data into 4 equal parts.

​

• Thus there are three quartiles known as Q1, Q2, and Q3.

​

​

• 25% of items of a have values less than Q1,

75% of the items have values less than Q3.

Quartiles

• Split ordered data into 4 Quarters.

​

​

​

​

Q1

Q2

Q3

Deciles :-

• Deciles are those values of the variable which divides the data into 10 equal parts.

​

• Thus there are nine deciles denoted by D1.D2,.........D9.

​

• 20% of items of a have values less than D2 .
• 40% of the items have values less than D4
• D7 will have 70% observation on its left side and 30% observation on its right side.

Percentile :-

• Percentile are those values of the variables, which divides the data into 100 equal parts.
• Thus their are 99 percentiles denoted by P1,P2,P26,P56........P99.
• 20% of items of a have values less than P20,
• 40% of the items have values less than P40

Computation of Partition Values

FORMULA FOR PARTITION VALUES

• In case of Quartile (Q) = ( N+1)

​

• In Case of Deciles (D) = (N+1)

​

• In case of Percentile (P) = (N+1)

​

• In the same way..............

4

10

100

FORMULA FOR PARTITION VALUES

• In case of 3^rd Quartile (Q3) = 3( N+1)

​

• In Case of 4^th Deciles (D4) = 4(N+1)

​

• In case of 28^th Percentile (P28)= 28(N+1)

​

And so on...

4

10

100

lets take an Example....

In Discrete series :-

​

Find out 1^st (Q1) and 3^rd (Q3) quartile , 4^th Deciles (D4) and 80^th Percentile (P80)

​

​

​

Come ...lets solve it...

​

​

Solution:-�Compute c.f. first.......

Q1 = size of (N+1)item => 51+1

4

4

=

Size of 13^th item

Size of 13^th item lies in the c.f. 14,whose variable is 4

Thus , Q1 = 4

Q3= size of 3(N+1) item

4

3 (51+1)

4

= 39^TH Item

=>

Size of 39^th item lies in the c.f. 46,whose variable is 6

Thus , Q3 = 6

D4= size of 4(N+1) item

10

=>

4 (51+1)

10

= 20.8^TH Item

Size of 20.8^th item lies in the c.f. 35,whose variable is 5

Thus , D4 = 5

P80= size of 80 (N+1) item

100

=>

80 (51+1)

100

= 41.6^TH Item

Size of 41.6^th item lies in the c.f. 46,whose variable is 6

Thus , P80 = 6

Hence......you found

Partition values :-

​

Q1 = 4

Q3 = 6

D4 = 5

P80 = 6

Same Way........

With the same way you can find out Partition

Values in individual

series as well

as continuous

series easily...

That is all in the part of Partition Values

Thank you

THANKS