31.
If the mode of the data is 34.5, find the missing frequency 'L':
Class
15 - 30
45-60
30-45
60-75
Frequency
2
7
f 3 7
Answers
Step-by-step explanation:
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Solution :-
Class Frequency
0 - 15 2
15 - 30 7
30 - 45 f
45 - 60 3
60 - 75 7
we know that,
- Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] * h
since mode is given as 34.5 . then, modal class is 30 - 45.
so, we have,
- l = lower limit of modal class = 30
- f1 = frequency of modal class = f
- f0 = previous frequency = 7
- f2 = next frequency = 3 .
- h = size of class = 15 .
Putting all values we get,
→ 34.5 = 30 + [(f - 7)/(2f - 7 - 3)] * 15
→ 34.5 - 30 = [(f - 7)/(2f - 10)] * 15
→ 4.5(2f - 10) = 15(f - 7)
→ 9f - 45 = 15f - 105
→ 15f - 9f = 105 - 45
→ 6f = 60
→ f = 10. (Ans.)
Hence, the missing frequency is 10.
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