21. Find the mean and median of the given data :-
Weight (in kg)- 40-45 , 45-50, 50-55, 55-60, 60-65, 65-70, 70-75.
Number of students- 2, 3, 8, 6, 6, 3, 2.
Answers
Weight ( in kg ) Fi Xi FiXi C.F
40-45 2 42.5 85 2
45-50 3 47.5 142.5 5
50-55 8 52.5 420 13
55-60 6 57.5 345 19
60-65 6 62.5 375 25
65-70 3 67.5 202.5 28
70-75 2 72.5 145 30
⅀Fi=30 ⅀FiXi=1715
So,
→ Mean = ⅀FiXi / ⅀Fi = 1715 / 30 = 57.16 (Ans)
Now, we have,
→ N = 30
→ N / 2 = 15
→ Median class = 55 - 60
So,
- L = 55
- f = 6
- cf = 13
- h = 60 - 55 = 5
therefore,
→ Median = l + {(N/2) - cf} / f} * h
→ Median=55 + {(15 - 13)/6} * 5
→ Median = 55 + (1/3) * 5
→ Median = 55 + 1.67
→ Median = 55 + 1.67 = 56.67 (Ans.)
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