Compute the mode of the following data:
Class Interval
Frequency
1-5
3
6-10
8
11-15
13
16-20
18
21-25
28
26-30
20
31-35
13
36-40
8
41-45
6
46-50
4
Mode $23.22$ .
If true then enter $1$ and if false then enter $0$

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Solution

Class
intervals Freq(Fi)

1-5 3

6-10 8

11-15 13

16-20 18

21-25 28

26-30 20

31-35 13

36-40 8

41-45 6

46-50 4

Total 121
$M o d e = l + \frac{(f_{m} - f_{m - 1})}{(f_{m} - f_{m - 1}) + (f_{m} - f_{m + 1})} \times w l i s t h e l o w e r c l a s s b o u n d a r y o f t h e m o d a l c l a s s i n t e r v a l; f_{m - 1} i s t h e f r e q u e n c y o f t h e g r o u p b e f o r e t h e m o d a l c l a s s i n t e r v a l . f_{m} i s t h e f r e q u e n c y o f t h e m o d a l c l a s s i n t e r v a l; f_{m + 1} i s t h e f r e q u e n c y o f t h e g r o u p a f t e r t h e m o d a l c l a s s i n t e r v a l . w i s t h e w i d t h o f t h e c l a s s i n t e r v a l . H e r e m o d a l r a n g e i s 21 - 25. l = 21, f_{m} = 28, f_{m - 1} = 18, f_{m + 1} = 20, w = 4 M o d e = 21 + \frac{28 - 18}{(28 - 18) + (28 - 20)} \times 4 = 21 + \frac{10 \times 4}{10 + 8} = 21 + \frac{40}{18} = 21 + 2.22 = 23.22$

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