find the sample variance, standard deviation, and range of the data.
7, 5, 9, 7, 2, 4, 3, 2, 3, 8
Solution:
Given that,
2,2,3,3,4,5,7,7,8,9
n = 10
The mean of sample is
x/n = (2 +2 + 3 +3 + 4 + 5 + 7 +7 +8 + 9 / 10)
= 50 / 10
= 5
The sample mean is 5
Sample variance is s^{2}
s^{2} = 1/(n-1)(x - )^{2}
^{= }1/(10 - 1) (2 - 5 )^{2}+ (2 - 5 )^{2}+ (3 - 5 )^{2}+ (3 - 5 )^{2} +( 4 - 5 )^{2} + (5 - 5 )^{2}+ (7 - 5 )^{2}+ (7 - 5 )^{2}+ (8 - 5 )^{2} +( 9 - 5 )^{2}
= 1/9 (9 + 9 + 4+ 4 + 1 + 0 + 4 + 4 + 9 + 16)
= 60 /9
= 6.67
The sample variance is = 6.67
b) Sample standard deviation is = s = s^{2}
Sample standard deviation is = s = 6.67
Sample standard deviation is = s = 2.58
c) The range = 9 - 2 = 7
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