12. The following table shows the distribution of weights of 100 candidates appearing for a
competition. Determine the modal weight.
50-55
55-60
Weight
(in kg)
60-65
65-70
70-75
75-80
no .of candidates
13
18
45
16
6
2
Answers
Answer:
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Step-by-step explanation:
Weight No. of candidates
50−55 13
55−60 10
60−65 45
65−70 16
70−75 06
75−80 02
The model weight is 60−65
We know,
mode=l+
2f−f
1
−f
2
f−f
1
×h
f=45 f
2
=16
f
1
=10 h=5
l=60
=60+
2×45−16−10
45−10
×5
=60+
56
27
×5
=60+
56
135
=60+2.4
=62.4
Answer:
The modal weight is 60-65
where,
lower limit of the modal class (l)= 60
size of the class interval assuming all class size to be equal (h)= 5
frequency of the modal class (F1)= 18
frequency of the class preceding the modal class (f0)=45
frequency of the class succeeding the modal class (F2)=16
We know that,
Mode= l+{f1-f0/2f1-f0-f2}*h
=60+{18-45/2*18-45-16}*5
=60+ {(-27)/36-61}*5
=60+{(-27)/(-25)}*5
=60+{27/5}
=60+5.4
=65.4kg