Page 159 - DMGT404 RESEARCH_METHODOLOGY

Unit 8: Descriptive Statistics

The highest frequency total in each of the six columns is identified and analysed to determine Notes
mode. We apply this method for determining mode of the above example.

X f (1) (2) (3) (4) (5) (6)
10 8
23
11 15 43
35
135
12 20
120
13 100 218
198
14 98 293
193
15 95 283
185
16 90 260
165
215
17 75
125
18 50 155
80
19 30
Analysis Table
V A R I A B L E
Columns 10 11 12 13 14 15 16 17 18 19
1 1
2 1 1
3 1 1
4 1 1 1
5 1 1 1
6 1 1 1
Total 0 0 0 3 4 4 2 1 0 0
Since the value 14 and 15 are both repeated maximum number of times in the analysis table,
therefore, mode is ill defined. Mode in this case can be approximately located by the use of the
following formula, which will be discussed later, in this unit.
Mode = 3 Median – 2 Mean
Calculation of Median and Mean

X 10 11 12 13 14 15 16 17 18 19 Total
f 8 15 20 100 98 95 90 75 50 30 581

C.f. 8 23 43 143 241 336 426 501 551 581
fX 80 165 240 1300 1372 1425 1440 1275 900 570 8767

+
æ 581 1ö 8767
Median = Size of ç è 2 ÷ ø th, i.e., 291st observation = 15. Mean = 581 = 15.09
 Mode = 3 × 15 – 2 × 15.09 = 45 – 30.18 = 14.82

Notes If the most repeated values, in the above analysis table, were not adjacent, the
distribution would have been bimodal, i.e., having two modes

LOVELY PROFESSIONAL UNIVERSITY 153