The amount of leaf protein (mg/g fresh weight) in soybean plants of a particular variety was determined for a sample of six plants, yielding the following data: 12.9, 15.5, 13.2, 7.5, 6.1, 8.9
Compute:
The sample variance
Solution:
Given that,
12.9, 15.5, 13.2, 7.5, 6.1, 8.9
n = 6
The mean of sample is
x/n = ( 12.9 + 15.5 + 13.2 + 7.5 + 6.1 + 8.9 / 6)
= 64.1 / 6
= 10.68
The sample mean is 10.68
Sample variance is s
s^{2} = 1/(n-1)(x - )^{2}
^{= }1/6-1 (12.9 - 10.68)^{2}+ (15.5 - 10.68)^{2}+ (13.2 - 10.68)^{2}+ (7.5 - 10.68 )^{2} +( 6.1 - 10.68)^{2} + ( 8.9 - 10.68)^{2}
= 1/5 (4.9284 + 23.2324 + 6.3504 + 10.1124 + 20.9764 + 3.1684)
= 68.7684 / 5
= 13.75
The sample variance is 13.75
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