A random sample of 40 smokers is classified in the following table:
Ages Frequency
[10-20) 4
[20-30) 6
[30-40) 12
[40-50) 10
[50-60) 8
Total 40
The variance is?
154.8718
160
144.6364
165.6543
To find the variance, we will first need to calculate the mean and then use the formula for variance.
Mean = Σ(x * f) / N
Where:
x = midpoint of the class interval
f = frequency of each interval
N = total number of observations
Midpoint of intervals:
[10-20) = 15
[20-30) = 25
[30-40) = 35
[40-50) = 45
[50-60) = 55
Mean = (15*4 + 25*6 + 35*12 + 45*10 + 55*8) / 40
Mean = (60 + 150 + 420 + 450 + 440) / 40
Mean = 1520 / 40
Mean = 38
Now, we can calculate the variance using the formula:
Variance = Σ(f * (x - mean)^2) / N
Using the midpoint values and the mean calculated above:
Variance = (4*(15-38)^2 + 6*(25-38)^2 + 12*(35-38)^2 + 10*(45-38)^2 + 8*(55-38)^2) / 40
Variance = (4*(-23)^2 + 6*(-13)^2 + 12*(-3)^2 + 10*(7)^2 + 8*(17)^2) / 40
Variance = (4*529 + 6*169 + 12*9 + 10*49 + 8*289) / 40
Variance = (2116 + 1014 + 108 + 490 + 2312) / 40
Variance = 6240 / 40
Variance = 156
The variance is 156.