Question

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee Frequency 800 200 2 900 600 Total: 2,500 The expected value is 1.52. Find the variance of the number of cups of coffee. O 0.76 0.87 1.17 1.37

Answer 1

Solution

Given that

Solution:

x	Frequency	fx	fx2
0	800	0	0
1	200	200	200
2	900	1800	3600
3	600	1800	5400
	n = 2500	$\sum$fx = 3800	$\sum$fx2 = 9200

The sample mean is $\bar x$

Mean $\bar x$   = ($\sum$fx / n) )

= 3800 / 2500

= 1.52

The sample mean is $\bar x$ = 1.52

The sample variance is S²

  S² =  ( $\sum$ fx² ) - (( $\sum$ fx)² / n ) n -1

=  (9200 ( (3800 )² / 2500 ) 2499

   = ( 9200- 5776 / 2499)

= (3424/ 2499 )

= 1.37

The sample variance = 1.37