Question

5) The population variance of the data set provided below is 18.7. Find k.

1.2k

1.6k

2.2k

2.9k

3.3k

Round your answer to two decimal places.

Answer 1

The population variance of the data set provided is 18.7

k = ?

1.2k

1.6k

2.2k

2.9k

3.3k

Mean =

=  

= k

= 2.24 k

population variance (²) =

= (1.2 k -2.24 k)² +(1.6 k -2.24 k)² +(2.2 k -2.24 k)+(2.9k - 2.24 k)²+(3.3 k - 2.24k)²   

= (-1.04k)² +(-0.64k)²+(-0.04k)²+(0.66k)²+(1.06k)²

= 1.0816 k ²+ 0.4096 k² +(1.6*10^-0.3) k² +0.4356k² +1.1236 k²

= 4.6504 k ² * 10^-0.3

=

=

=

= 0.46614 k ²

But given   = 18.7

0.46614 k ² = 18.7

k ² =

=

k = 9.277

the value of k = 9.277