Given that the mean height of a group of students is 67.45 inches. Find out the missing frequencies for that following Incomplete distribution of height of 100 students.
Answers
The complete data is,
findout the missing frequencies from the following data,given that A.M=67.45 inches :height(inches)-60-62| 63-65|66-68|69-71|72-74|Total|
no.of student- 5 | 18 |f3 |f4 |8 |100 |
N = 100
5 + 18 + f3 + f4 + 8 = 100
31 + f3 + f4 = 100
f3 + f4 = 100 - 31
f3 + f4 = 69 .........(1)
Class Interval Frequency Mid-Value fidi
60-62 5 61 -2 -10
63-65 18 64 -1 -18
66-68 f3 67 0 0
69-71 f4 70 1 f4
72-74 8 73 2 16
Total ∑f = N = 31 + f3 + f4 A = 67 - ∑ fd = –12 + f4
Arithmetic mean
= 67.45 (given)
(-12 + f4) × 3 = (67.45 - 67) × 100
-12 + f4 = 15
f4 = 15 + 12
∴ f4 = 27
Using (1) we have,
f3 + 27 = 69
f3 = 69 - 27
∴ f3 = 42
Therefore, the missing frequencies are 27 and 42
Answer:
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