calculate the standard deviation of the following series. marks more than: 0 , 10 , 20 , 30 , 40 , 50 , 60 , 70 no. of students : 100 , 90 , 75 , 50 , 25 , 15 , 5 , 0
Answers
Given : marks more than: 0 , 10 , 20 , 30 , 40 , 50 , 60 , 70
no. of students : 100 , 90 , 75 , 50 , 25 , 15 , 5 , 0
To Find : standard deviation
Solution:
Convert more than frequency
x f f.x
5 10 50
15 15 225
25 25 625
35 25 875
45 10 450
55 10 550
65 5 325
100 3100
Mean = 3100/100 = 31
x f (x-μ) (x-μ)² f.(x-μ)²
5 10 -26 676 6760
15 15 -16 256 3840
25 25 -6 36 900
35 25 4 16 400
45 10 14 196 1960
55 10 24 576 5760
65 5 34 1156 5780
100 25400
SD = √∑f.(x-μ)²/∑f
= √(25400 /100)
= √ 254
= 15.937
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