Respuesta :
Answer:
The variance of the number of cups of coffee is 0.96
Step-by-step explanation:
We are given the following in the question:
Cups of coffee,x: 0 1 2 3
Frequency,f(x): 700 900 600 300
Formula:
[tex]E(x) = \dfrac{\sum fx}{\sum f}\\\\\text{Variance} = \dfrac{\sum fx^2}{\sum f} - (E(x) )^2[/tex]
Putting values, we get,
[tex]E(x) = \dfrac{0(700) + 1(900) + 2(600) + 3(300)}{2500} = \dfrac{3000}{2500} = 1.2\\\\\dfrac{\sum fx^2}{\sum f} = \dfrac{0(700) + 1(900) + 4(600) + 9(300)}{2500}=2.4[/tex]
Variance =
[tex]2.4 - (1.2)^2 = 0.96[/tex]
Thus, the variance of the number of cups of coffee is 0.96
The variance on the number of cups of coffee is 0.9604
Data;
- Total number of people = 2500
- f1 = 700
- f2 = 900
- f3 = 600
- f4 = 300
Variance
To solve the variance, we have to find the mean of the data.
[tex]mean(\mu) = \frac{\sum _f_*_x}{\sum _F} \\[/tex]
Let's substitute the values into the formula
[tex]\mu = \frac{0*700 + 1 * 900 + 2 * 600 + 3 * 300 }{2500}\\\mu = \frac{3000}{2500} \\\mu = 1.2[/tex]
The formula of variance is given as;
[tex]V = \frac{\sum _f_*_x_^2 - n\mu ^2}{n-1} \\V = \frac{0^2 * 700 + 1^2 * 900 + 2^2 * 600 + 3^2 * 300 - 2500 * 1.2^2}{2500-1} \\V = \frac{0+900+(4*60)+(9*300)-2500*1.44}{2499} \\V = 0.9604[/tex]
The variance on the number of cups of coffee is 0.9604
Learn more on variance here;
https://brainly.com/question/12287318
