Question

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

Answer 1

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

s² = 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