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 0 700 1 900 2 600 3 300 2,500 Refer to Exhibit 5-7. The variance of the number of cups of coffee is _____.

Answer 1

Answer: V(X) = 0.96

Step-by-step explanation: Variance is defined as the average of the squared difference from the sample or population mean.

For a discrete frequency distribution is calculated following the steps:

1) Determine expected value or mean:

$E(X)=\frac{\Sigma xf}{\Sigma f}$

$E(X)=\frac{0(700)+1(900)+2(600)+3(300)}{2500}$

E(X) = 1.2

2) Multiply frequency and the squared difference of x and expected value:

$f(x-E(X))^{2}$

$700(0-1.2)^{2}=1008\\900(1-1.2)^{2} = 36\\600(2-1.2)^{2} = 384\\300(3-1.2)^{2} = 972$

3) Add them:

$\Sigma [f(x-E(X))^{2}]$ = 1008 + 36 + 384 + 972 = 2400

4) Divide the sum per frequency total:

$V(X)=\frac{\Sigma [f(x-E(X))^{2}]}{\Sigma f}$

$V(X)=\frac{2400}{2500}$

V(X) = 0.96

The variance of the number of cups of coffee is 0.96.