ppt on measures of central tendency - mode , harmonic mean and geometric mean

1. MEASURES OF CENTRAL TENDENCY
MODE, HARMONIC MEAN & GEOMETRIC MEAN
DR.S.MALINI
ASSOCIATE PROFESSOR
DEPARTMENT OF ECONOMICS
ETHIRAJ COLLEGE FOR WOMEN, CHENNAI

2. MODE
• Occurs with the maximum frequency
• Denoted by the symbol M0
• It shows the centre of concentration
of the frequency in around a given
value
• In a normal distribution mode is
Unimodal
• Grouping table is used to determine
Mode graphically
• If the distribution is bimodal, then
mode is determined empirically, by
the formula
Mode = 3 Median – 2 Mean

3. INDIVIDUAL OBSERVATIONS
Individual Observations
Ex. Consider the following 10 observations
8 is the modal value as it has occurred thrice
2 5 8 6.3 2 7 10 8 3 8

4. MODE DISCRETE SERIES
X 18 20 24 28
f 45 85 37 26
X 7 8 9 10 11 12 13
f 5 16 25 40 44 58 12
X 15 16 17 18 19 20 21 22
f 10 9 14 17 18 13 12 15

5. MODE – GROUPING TABLE STEPS
Column -1
• Actual Frequencies against the Class intervals or the series
Column -2
• Frequencies are grouped in Two’s
Column-3
• Excluding the first frequency, the other frequencies are grouped in
two’s
Column-4
• Frequencies are grouped in three’s
Column-5
• Excluding the First frequency, the other frequencies are grouped in
three’s
Column-6
• Excluding the first two Frequencies, the remaining frequencies are
grouped in three’s

6. MODE - GROUPING TABLE

7. ANALYSIS TABLE
10 11 12 13 14 15 16 17 18
Col 1 1
Col 2 1 1
Col 3 1 1
Col 4 1 1 1
Col 5 1 1 1
Col 6 1 1 1
Total 1 3 5 4 1

8. MODE- CONTINUOUS SERIES
Class Interval Frequency
100 - 200 10
200 - 300 15
300 - 400 17
400 - 500 6
500 - 600 10

9. HARMONIC MEAN

10. HARMONIC MEAN -DISCRETE
SERIES
Marks Frequency f/x
20 3 0.15
25 4 0.15
30 7 0.23
35 8 0.22
40 6 0.15
N=28 0.91

11. HARMONIC MEAN – CONTINUOUS
SERIES
C I f Midpoint f/m
5-10 1 7.5 0.133
10-15 9 12. 0.72
15-20 29 17.5 1.657
20-25 54 22.5 2.4
25-30 11 27.5 0.4
30-35 5 32.5 0.154
N= 109 5.464

12. GEOMETRIC MEAN – INDIVIDUAL
OBSERVATIONS
x Log x
60 1.778
100 2.000
45 1.653
65 1.813
48 1.681

13. GEOMETRIC MEAN –DISCRETE
SERIES
x f Log x f Logx
50 5 1.699 8.495
63 10 10.799 17.99
65 5 1.813 9.065
130 15 2.114 31.71
135 15 2.130 31.95
Total 50 9.555 99.21

14. GEOMETRIC MEAN –CONTINUOUS SERIES
C.I f Midpoint (m) Log m F logm
60 - 80 22 70 1.845 40.59
80 -100 38 90 1.954 74.25
100 -120 45 110 2.041 91.85
120 -140 35 130 2.114 73.99
140 -160 20 150 2.176 43.52
Total 160 324. 2

15. Thank You