This document discusses a quantitative techniques course for a B.Com program. It covers measures of central tendency like mean, median, and mode. The learning objectives are to understand different measures of central tendency and dispersion. The learning outcomes are to differentiate, determine, and identify relationships between averages, and apply measures of dispersion to sample data. The session covers problems calculating missing frequencies and variables in the mean under discrete series. It provides two examples of finding missing values when the mean is given. The document concludes with multiple choice questions reviewing the material.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 38

2. RECAP
• Mean, Median & Mode Under Continuous 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 - 38
• Missing Frequencies & Variables in Mean Under
Discrete Series Problems------ 01

6. Missing frequencies under discrete series
Ex ; 1. Find missing frequency when Mean = 18
X: 5, 10, 15, 25, 30
F: 2, 6, f , 5, 4
Solution: X F fx
5 2 10
10 6 60
15 f 15f
25 5 125
30 4 120
N = 17 + f ∑fx = 315 + 15f

7. CONTD
𝑋 = ∑fx/n, ∑fx = 315 + 15f, n = 17+f, 𝑋 = 18
18 = 315 + 15f / 17+f
18 (17 + f) = 315 + 15f
306 + 18f = 315 + 15f
18f – 15f = 315 – 306
3f = 9, f =9/3, f = 3
Ex; 2. Find Missing value when mean wage 111.85
Wage: 100, 110, X, 125, 130
workers 15, 12, 18, 12, 08
Solution; see next page

8. CONTD
Ascertaining of missing wages
WAGES (X) WORKERS(F) FX
100 15 1500
110 12 1320
X 18 18X
125 12 1500
130 08 1040
N = 65 ∑FX = 5360 + 18X

9. CONTD
∑FX = 5360 + 18X, N= 65,
𝑋 = ∑FX/N
111.85 = 5360 + 18X/ 65
111.85 X 65 = 5360 + 18X
7270.25 = 5360 + 18X
7270.25 – 5360 = 18X
1910.25 = 18X
X = 1910.25/18
X =106.13 OR 106

10. SUMMARY
As we already discussed and learnt today on Measures
of Central Tendency ( Averages)
• Missing Frequencies & Variables in Mean Under
Discrete Series Problems ------ 01

11. MCQs
1 . The distribution in which mean = 50 and median =48
mode will be ____________
a) 44
b) 24
c) 34
d) None of these
2. Relationship of empirical
a) SK=mean – mode/ S.D
b) Z = 3Me - 2 𝑋
c) Mode = 3median – 2mean
d) Both b and c

12. MCQs
3 . If mean = 35 and Mode = 32 and Median = ?
a) 34
b) 32
c) Zero
d) None of these
4. If median = 21.5, Mode = 22 and Mean =?
a) 20
b) 19
c) 21.25
d) None of these

13. MCQs
5 . The relationship of empirical between averages
a) Some time equal
b) Never equal
c) Always equal
d) None of these

14. CONTD
ANSWERS
1. A
2. D
3. A
4. C
5. A

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