Question

The ages? (in years) of a random sample of elementary school kids are shown. Determine the? range, variance, and standard deviation of the sample data set. 5 7 9 6 7 8

Answer 1

Solution:

Given that,

5,6,7,7,8,9

The? range = Maximun value - Minimum value

= 9 - 5

= 4

The? range is 4

The mean of sample is   

x/n =  (5 + 7 + 9 + 6 + 7+ 8 / 6)

= 42 / 6

= 7

The sample mean is 7

Variance = s²

s² = 1/(n-1)(x - )²

⁼  1/5 (5 - 7)²+ (7 - 7 )²+ ( 9 - 7 )²+ ( 6 - 7 )² +( 7 - 7 )²+ (8 - 7 )² )

= 1/5 (4+0+4+1+0+1 )

= 10/5

= 2.

Variance is 2

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/5 (5 - 7)²+ (7 - 7 )²+ ( 9 - 7 )²+ ( 6 - 7 )² +( 7 - 7 )²+ (8 - 7 )² )

= 1/5 (4+0+4+1+0+1 )

= 10/5

= 2.

= 1.41

Sample standard deviation is 1.41