52. The mean of the following frequency distribution is 43.75 :
Class. Frequency
0-10. 8
10-20. 4
20-30. 20
30-40. 45
40-50. 64
50-60. 32
60-70. f
70-80. 8
80-90. 2
90-100. 2
Find the missing frequency f.
Answers
Answer:
Mean=Sum of all observations/No. of all observations
43.75=8+4+20+45+64+32+f+8+2+2/10
43.75=185+f/10
185+f=43.75×10
185+f=437.5
f=437.5-185
f=252.5
Solution :-
Class Fi Xi FiXi
0-10 8 5 40
10-20 4 15 60
20-30 20 25 500
30-40 45 35 1575
40-50 64 45 2880
50-60 32 55 1760
60-70 f 65 65f
70-80 8 75 600
80-90 2 85 170
90-100 2 95 190
⅀Fi=185+f ⅀FiXi=7775+65f
we know that,
- Mean = ⅀FiXi / ⅀Fi
so,
→ (7775 + 65f) /(185 + f) = 43.75
→ 7775 + 65f = 8093.75 + 43.75f
→ 65f - 43.75f = 8093.75 - 7775
→ 21.25f = 318.75
→ f = (318.75/21.25)
→ f = 15 .(Ans.)
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