Calculate the standard deviation and mean diameter of the circles.
Calculate the standard deviation and mean diameter of the circles.
|
Classes |
xi |
yi = (xi – 42.5)/4 |
f i |
f i y i |
f i y i2 |
|
32.5-36.5 |
34.5 |
-2 |
15 |
-30 |
60 |
|
36.5-40.5 |
38.5 |
-1 |
17 |
-17 |
17 |
|
40.5-44.5 |
42.5 |
0 |
21 |
0 |
0 |
|
44.5-48.5 |
46.5 |
1 |
22 |
22 |
22 |
|
48.5-52.5 |
50.5 |
2 |
25 |
50 |
100 |
|
Total |
100 |
25 |
199 |
Mean diameter of the circles = 
= 
= 43.5
Variance (σ 2) = [(4)2/100][199 – 625/100] = 30.84
Hence the Standard Deviation is (σ ) = 
= 5.55
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