Question

12. From the following data, determine the mode by grouping method-
Size
7
8
9
10
11
12
13
14
15
16
17
Frequency
2
3
6
12
20
24
25
7
5
3
1​

Answer 1

Answer:

Same as

Size of the item f

10−15 4

15−20 8

20−25 18

25−30 30

30−35 20

35−40 10

40−45 5

45−50 2

Modal class is 25−30 since it has the maximum frequency.

Lower limit of the modal class l=25

Frequency of the modal class f=30

Frequency of the preceding modal class f

1

=18

Frequency of the class reducing the modal class f

2

=20

Class width c=5

Mode =l+(

2f−f

1

−f

2

f−f

1

)×c

=25+(

60−18−20

30−18

)×5=25+

22

12×5

=25+

22

60

=25+2.73=27.73

Mode =27.73