Different Analytical Techniques used in Statistics

1. SL NAME
1 Md. Humaun Rashid
2 Md. Sohel Rana
1
Different Analytical
Techniques in Management
Presented ByPresented By
Business Administration DepartmentBusiness Administration Department
East West UniversityEast West University

2. Preface…Preface…
From this real data set we will process of making a frequency
distribution taking Class Interval (CI), graphical presentation of the data
set , calculating Measure of Central Tendency (Mean, Mode, Median),
Measures of Dispersion.
2
For the purpose of our presentation we are colleting theFor the purpose of our presentation we are colleting the
real data set from SCHOLASTICA LIMITED. HRreal data set from SCHOLASTICA LIMITED. HR
Department of SCHOLASTICA LIMITED organized anDepartment of SCHOLASTICA LIMITED organized an
Business English Course for their ManagementBusiness English Course for their Management
Employees for enrich the communication skills .Employees for enrich the communication skills .
The marks obtained by 30 employees are given below:
32 33 55 47 21 50 27 26 24 33 62 42 38 15 45
32 44 68 48 49 40 52 30 17 44 58 37 48 39 42

3. Frequency Distribution:Frequency Distribution:
The marks obtained by 30 employees are given below:The marks obtained by 30 employees are given below:
From the collected real data where-
Expected Number of Class:
K =1+3.322Xlog10n
=1+3.322X1.48
= 5.9
The Suggested Class Interval (CI)is:
Class Interval CI= Highest Value-Lowest Value/k
= 68-15/5.9
= 8.9
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32 33 55 47 21 50 27 26 24 33 62 42 38 15 45
32 44 68 48 49 40 52 30 17 44 58 37 48 39 42

4. To be continued…To be continued…
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Class Interval
(CI)
Tally Frequency
(f)
Mid Value
X
Xf Cf
10-20 ll 2 15 30 2
20-30 llll 4 25 100 6
30-40 llll lll 8 35 280 14
40-50 llll llll 10 45 450 24
50-60 llll 4 55 220 28
60-70 ll 2 65 130 30
We will take the round number 10 as the CI.

5. Histogram for Marks ObtainedHistogram for Marks Obtained
0
2
4
6
8
10
12
10 20 30 40 50 60 70
Marks Obtained
Frequency
5

6. Measure of Central Tendency (Mean)Measure of Central Tendency (Mean)
The mean of a Frequency Distribution can
be computed using the below formula:
Mean X= Xf/ f = Xf/nƩ Ʃ Ʃ
=1210/30
=40.333
Where,
X: Class Marks or Mid point of the class
f: Frequency in the class
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7. Measure of Central Tendency (Median)Measure of Central Tendency (Median)
To determine the median class for this data set mentioned
earlier we have prepared a frequency distribution and divide
the total number of data values by 2. n=30/2 =15.
Yellow marked column is the median class as 15th
value lies in
this class. Median is computed using the below formula-
Median= L+[n/2-cf)/f]Xci
= 40+[30/2-14)/10]X10
=41
Here,
L = lower limit of the median class
Cf =cumulative frequency pre-median class
f = frequency of the median class
Ci =class interval
n = total number of observation
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8. Measure of Central Tendency (Mode)Measure of Central Tendency (Mode)
 Since the highest frequency 10 lies in the class 40-50, hence
the modal class in 40-50.
Mode calculation is done using the following formula:
Mode=L+[∆1/(∆1+ ∆2)]Xci
= 40+[2/(2+6)]Xci
= 43.33
Here,
L = lower limit of the modal class
∆1= difference between frequencies modal and pre-modal class
∆2= difference between frequencies of modal and post-modal
class
Ci = class interval
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9. Measures of DispersionMeasures of Dispersion
 It deals with spread of the data
 A small value of the measure of dispersion indicates that data are
clustered closely
 A large value of dispersion indicates the estimate of central
tendency is not reliable
We will considering Measures of Dispersion (Range) for the data set.
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10. Measures of Dispersion (Range)Measures of Dispersion (Range)
The Range is the difference between highest value and lowest
value of the data set. Here Range is-
Range= Highest Value-Lowest Value
= 68-15
= 53
10
Class Interval
(CI)
Frequency
(f)
Mid Value
X X-X lX-Xl flX-Xl (X-X)2
10-20 2 15 -25 25 50 625
20-30 4 25 -15 15 60 225
30-40 8 35 -5 5 40 25
40-50 10 45 5 5 50 25
50-60 4 55 10 10 40 100
60-70 2 65 25 25 50 625
30 290 1625

11. Measures of Dispersion (Mean Deviation)Measures of Dispersion (Mean Deviation)
Mean Deviation is the arithmetic
mean of the absolute values of the
deviations of the observations from
the arithmetic.
Mean Deviation = f lX-Xl/ fƩ Ʃ
= 290/30
= 9.67
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Here,
X= X/nƩ
= 240/6
= 40

12. Measures of Dispersion (Variance)Measures of Dispersion (Variance)
The formula for the calculation of
variance is-
Variance
= 4250/30
=141.66
Here,
f= class frequency
X= class mid point
X= arithmetic mean
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( )
f
XXf
S
Σ
−
=
∑
2
2

13. Measures of Dispersion (Standard DeviationMeasures of Dispersion (Standard Deviation))
Standard Deviation (SD) is the positive square
root of the variance and can be calculated in
the following way-
=11.90
13
66.141
)( 2
2
=






Σ
−Σ
==
f
XXf
SS

14. Coefficient of Correlation andCoefficient of Correlation and
analyzing Regressionanalyzing Regression
 Correlation Analysis is the group of statistical techniques used to
measure the strength of the relationship (correlation) between
two variables.
 In regression analysis an equation is developed to express the
relationship between dependent and independent variables
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15. To be Continued….To be Continued….
 Determining the coefficient of correlation and analyzing
regression we have been collected the age-wise salary
range data from the same organization (SCHOLASTICA
LIMITED).
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Age Range Salary Range
25 30000
30 36000
32 42000
40 45000
48 50000

16. CorrelationCorrelation
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X
Age
Y
Salary
X-X Y-Y (X-X)X(Y-Y) (X-X)2 (Y-Y)2
25 3000 -10 -1060 10600 100 1123600
30 3600 -5 -460 2300 25 211600
32 4200 -3 140 -420 9 19600
40 4500 5 440 2200 25 193600
48 5000 13 940 12220 169 883600
20300 0 0 26900 328 2432000
X= X/nƩ
=175/5
=35
Y= Y/nƩ
=20,300/5
=4060
2432000328X
26900
=
=0.95 This value indicate perfect and strong correlation.

17. RegressionRegression
26900
328
= 82.0122
a= 4060 - 82.0122 X 35
= 1189.573
Y= 1189.573 + 82.0122X
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18. Thanks to everyoneThanks to everyone
forfor
being with us….!being with us….!
We are highly appreciating would you
want to know any queries regarding our
presentation…………….???
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19. ReferenceReference
 http://www.css.edu/
 http://www.purplemath.com/modules/meanmode.htm
 https://en.wikipedia.org/wiki/Central_tendency
 http://onlinestatbook.com/2/summarizing_distributions/
what_is_ct.html
 https://statistics.laerd.com/statistical-guides/measures-
central-tendency-mean-mode-median.php
 http://www.law.uchicago.edu/files/files/20.Sykes_.Regres
sion.pdf
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