The mean of the following frequency distribution is 145 find the value of f1 and f2
Answers
Given : frequency distribution Mean is 145
To find : f1 & f2
Solution:
100 - 120 10
120 - 140 f1
140-160 f2
160-180 15
180- 200 5
Total = 80
10 + f1 + f2 + 15 + 5 = 80
=> f1 + f2 = 80 - 30
=> f1 + f2 = 50 - eq 1
100 - 120 , mean = (100 + 120)/2 = 110
frequency = 10
so SubTotal = 110 * 10 = 1100
Similarly
120-140 SubTotal = 130 * f1
140 -160 SubTotal = 150 * f2
160-180 SubTotal = 170*15 = 2550
180 - 200 SubTotal = 190*5 = 950
Total = 1100 + 130f1 + 150f2 + 2550 + 950 = 4600 + 130f1 + 150f2
Total frequencies = 80
Mean = Total / Total Frequencies
=> 145 = (4600 + 130f1 + 150f2)/80
=> 11600 = 4600 + 130f1 + 150f2
=> 130f1 + 150f2 = 7000
=> 13f1 + 15f2 = 700 - eq 2
Eq 2 - 13Eq1
13f1 + 15f2 - 13f1 - 13f2 = 700 - 650
=> 2f2 = 50
=> f2 = 25
Putting in eq 1
f1 + 25 = 50
=> f1 = 25
f1 & f2 = 25
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