This document outlines the key topics and objectives of a Quantitative Techniques course for a B.Com program. The learning objectives are to understand measures of central tendency and dispersion such as mean, median, mode, range, mean deviation, standard deviation, and quartile deviation. Example problems are provided to calculate range, quartile deviation, and the coefficient of quartile deviation from wage distribution data. Multiple choice questions are also included as a review of the concepts taught.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 43

2. RECAP
• Range, Quartile Deviation and Co efficient Under
Individual and Discrete Series Problems------ 02

3. LEARNING OBJECTIVES
• After reading this chapter, a student will be
understand different measures of central tendency
and Dispersion, i.e., Arithmetic Mean,Mean,Mode,
Geometric and Harmonic mean & Range, Mean
Deviation, Standard Deviation, Quartile Deviation,
Co efficient of variation

4. LEARNING OUTCOMES
• After the Chapter, The Students Shall be able to
Differentiate, Determine, and Identify the
relationships among Averages under Different
Series of Data and too State the Merits and
Demerits of Three Measures. The Students will
apply Measures of Dispersion to Sample Population
Data by Contrasting the Values of Standard
Deviation & The Mean Deviation, Synthesizing the
Mean,Standard,and Quartile Deviations into a
Useful Description of a Set of Data

5. SESSION - 43
• Range, Quartile Deviation and Co efficient Under
Continuous Series Problems - 02

6. Range and Quartile Deviation
Example; 1
Calculate Range and Quartile deviation and coefficient
of quartile deviation from the following distribution.
Weekly Wages 5-7, 8-10, 11-13, 14-16, 17-19
No. of Workers 14, 24, 38, 20, 04
Solution; the above data convert into inclusive into
exclusive method (i.e., 4.5 – 7.5, 7.5 – 10.5 so on)

7. CONTD
Calculation of Range and Quartile deviation and
coefficient of quartile deviation
wages frequency C.F
4.5 -7.5 14 14
7.5 – 10.5 24 38
10.5 – 13.5 38 76
13.5 – 16.5 20 96
16.5 – 19.5 04 100
N = 100

8. Contd
Q1 = L + N/4 – CF x C , Q3 = L + 3(N/4) – CF x C
f f
The item of N/4 = 100/4 =25th lies in Class interval 7.5 –
10.5, L= 7.5, C.F =14, F=24, C = 3
Q1 = 7.5 + 25 – 14 x 3 Q1 = 7.5+ 11/24 x 3
24 Q1 = 8.875 OR 9
The item of 3(N/4) = 3(100/4)= 300/4 =75th item lies in
Class interval 10.5 – 13.5, L =10.5, CF =38, f =38, C =3
Q3 =10.5 + 75 – 38 x C, Q3 = 10.5 + 37/38 x 3
38 Q3 = 13.42

9. CONTD
R = L – S
R = 19.5 – 4.5 =15 Q3 – Q1
Co efficient of Q.D = Q3 + Q1 = 13.42 – 9/13.42 + 9
= 4.42/ 22.42 = 0.197
QUARTILE DEVIATION = Q3 – Q1/2 = 13.42 – 9/2
= 2.21
Co efficient of Range = L – S/L + S = 19.5 – 4.5/ 19.5 +4.5
= 0.625

10. CONTD
Calculate quartile deviation from the following
Solution:
QUARTILE DEVIATION = Q3 – Q1/2
Q1 = L + N/4 – CF x C , Q3 = L + 3(N/4) – CF x C
f f
To compute quartiles, Qj or Q1 OR Q3 class = (Nth/4)
item

11. CONTD

12. CONTD
QUARTILE DEVIATION = Q3 – Q1/2
Quartile Deviation = 37.03 – 14.1/2 = 11.465
Q3 – Q1
Co efficient of Q.D = Q3 + Q1
= 37.03 – 14.1/ 37.03 + 14.1
= 0.22

13. MCQs
I. If the maximum value in a series is 25 and its range is 15,
the maximum value of the series is:
(a) 10 (b) 15 (c) 25 (d) 35
II. Half of the difference between upper and lower quartiles is
called:
(a) Interquartile range (b) Quartile deviation (c)
Mean deviation (d) Standard deviation
III. If Q3=20 and Q1=10, the coefficient of quartile deviation
is:
(a) 3 (b) 1/3 (c) 2/3(d) 1

14. MCQs
IV. If the observations of a variable X are, -4, -20, -30, -44
and -36, then the value of the range will be:
(a) -48 (b) 40 (c) -40 (d) 48
V. Which measure of dispersion can be computed in
case of open-end classes?
(a) Standard deviation (b) Range (c) Quartile
deviation (d) Coefficient of variation

15. REFERENCES
• S.P. Gupta, Sultan Chand and Sons Publications, 2017
• S. C. Gupta, Himalaya Publishing House,
Fundamentals of Statistics, 2018
• R.S.N Pillai and Bagavathi, S.Chand publications, 2010

16. THANK YOU