Respuesta :
Answer:
Population variance 579
Population standard deviation 24
Step-by-step explanation:
The average estimated hours a person in the United States spent playing video games per year from 2002 to 2012 were 71, 80, 82, 78, 80, 91, 107, 121, 125, 131, and 142.
The population variance is given by:
[tex]\sigma^2=\frac{\sum(x-\mu)^2}{n}[/tex]
[tex]\mu=\frac{71+80+82+78+80+91+107+121+125+131+142}{11}[/tex]
[tex]\mu=\frac{1108}{11}[/tex]
This implies that:
[tex]\sigma^2=\frac{(71-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+(82-\frac{1108}{11})^2+(78-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+...+(142-\frac{1108}{11})^2}{11}[/tex]
[tex]\sigma^2=\frac{70006}{121} =579[/tex] to the nearest whole number
The population standard deviation is
[tex]\sigma=\frac{\sqrt{70006} }{11}=24[/tex] to the nearest whole number.
Answer:
Variance = 579 and Standard deviation = 24
Step-by-step explanation:
The given data set is the average estimated hours of a person in the U.S. spent playing video games per year from 2002 to 2012.
71, 80, 82, 78, 80, 91, 107, 121, 125, 131, 142.
We have to find the variance and standard deviation.
Formula for standard deviation :
[tex]\sqrt{\frac{\sum (x-\bar{x})}{n}}[/tex]
Using the step by step approach to find the standard deviation.
1. Calculate the mean
[tex]\bar{x}=\frac{\sum x}{n}[/tex]
= [tex]\frac{1108}{11}[/tex]
= 100.73
2. Subtract the mean from each value and square them then add all the squared result.
Time (x) [tex]x-\bar{x}[/tex] [tex](x-\bar{x})^{2}[/tex]
71 -29.73 883.8729
80 -20.73 429.7329
82 -18.73 350.8129
78 -22.73 516.6529
80 -20.73 429.7329
91 -9.73 94.6729
107 6.27 39.3129
121 20.27 410.8729
125 24.27 589.0329
131 30.27 916.2729
142 41.27 1,703.2129
6,364.1819
3. To calculate Variance (S²) divide this number by the total number of the data
Variance (S²) = [tex]\frac{6364.1819}{11}[/tex]
Variance = 578.56 ≈ 579
4. For standard deviation
Standard deviation = [tex]\sqrt{579}[/tex]
= 24.0624188 ≈ 24
Variance = 579 and Standard deviation = 24
