Given the following data
25 26 21 19 30 32 25 24 23
Calculate the
sample variance.
A)14.7
B)16.5
C)15.4
D)13.2
To calculate the sample variance, we first need to calculate the mean of the data set:
Mean = (25+26+21+19+30+32+25+24+23) / 9
Mean = 225 / 9
Mean = 25
Next, we need to calculate the squared differences from the mean for each data point, then sum those squared differences, and divide by n-1 (in this case, 9-1=8) to get the variance:
(25-25)^2 = 0
(26-25)^2 = 1
(21-25)^2 = 16
(19-25)^2 = 36
(30-25)^2 = 25
(32-25)^2 = 49
(25-25)^2 = 0
(24-25)^2 = 1
(23-25)^2 = 4
Sum of squared differences = 0 + 1 + 16 + 36 + 25 + 49 + 0 + 1 + 4 = 132
Variance = Sum of squared differences / (n-1)
Variance = 132 / 8
Variance = 16.5
Therefore, the sample variance is 16.5.
The correct answer is B) 16.5.