This document discusses a quantitative techniques course for a B.Com program. It covers measures of central tendency and dispersion, including the mean, median, mode, and standard deviation. The learning objectives are to understand these concepts and apply them to sample data. The session discusses calculating the mean, median, and mode for individual and discrete data series. It provides an example of calculating these values for a set of wage and employee data. Multiple choice questions review key aspects of the measures discussed.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 36

2. RECAP
• Mode Under Individual,Discrete & 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 - 36
• Mean, Median & Mode Under Individual and
Discrete Series Problems----------------------02

6. Mean Median and Mode Under Individual series
Calculate Mean, Median and Mode
ANS; 𝑋 = 𝑋/ N 𝑋 = 𝑓𝑥/ N
𝑋 = 2 + 4 + 13 + 6 + 8 + 10 + 12 + 10 + 17 + 10 + 21 +
10 + 18 + 27. N = 14
𝑋 = 168 / 14, 𝑋 = 12
The above data should be arranged in ascending order
while calculating median
2, 4, 6, 8, 10, 10, 10, 10, 12, 13, 17, 18, 21, 27
Me = N + 1/ 2, Me = 14 + 1 / 2, Me = 15 / 2, Me = 7.5th
Item, Me = 7th and 8th item , Me = 10 + 10 / 2 = 10
Mode = 10 is most repeated value 4 times in above data

7. Mean Median and Mode Under Discrete Series
Calculate Mean, Median and Mode 𝑋 = 𝑓𝑥/ N
ANS: 𝑋 = 𝑓𝑥/ N
Me = N + 1 / 2
Z = the variable which has highest frequency
Note ; while we calculating median and partition values
the data should be arranged in ascending order. In above
case no need to arrange because data is ascending

8. CONTD
Wages (X) No of persons
(F)
FX LCF
15 03 45 03
20 19 380 22
25 16 400 38
30 25 750 63
35 04 140 67
40 06 240 73
45 05 225 78
Z = 30 , the
variable which
has highest
frequency (25) is
mode
N = 78 𝒇𝒙 =2180
𝑋 = 𝑓𝑥/ N
𝑋 = 2180/ 78
𝑿 =27.94 or 28
Me = N + 1 / 2
Me = 78 + 1 / 2
Me = 79 / 2
Me = 39 . 5th item
lies in 63 LCF
So, Me = 35

9. SUMMARY
As we already discussed and learnt today on Measures
of Central Tendency ( Averages)
• Mean, Median & Mode Under Individual and Discrete
Series Problems----------------------02

10. MCQs
1 . The most commonly used measure of Central
tendency is
a) Mean
b) Median
c) Mode
d) None of these
2. What is the median for the numbers, 4,5,6,8,9,11,12
a) 8
b) 9
c) 10
d) 6

11. MCQs
3 . What is the mode for the numbers 4,5,6,11,9,11,12
a) 11
b) 12
c) 5
d) None of these
4. Which one of the following is not uniquely defined
a) Mean
b) Median
c) Mode
d) None of these

12. MCQs
5 . The values of mean, median and mode can be
a) Some time equal
b) Never equal
c) Always equal
d) None of these

13. CONTD
ANSWERS
1. A
2. A
3. A
4. C
5. A

14. 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

15. THANK YOU