Show work and solution. Also include correct notation. At the end of 2016, the average number...

Show work and solution. Also include correct notation.

At the end of 2016, the average number of businesses per county in Nebraska was 1,640. The businesses benefit from a state unemployment rate that is historically lower than the nation as a whole. Below is a partial list of counties in Nebraska and the respective number of businesses in operation at the end of 2016:

County # of Businesses
Custer 1,126
Sherman 279
Howard 454
Hall 5,085
Adams 2,794
Buffalo 3,992
Kearney 611
Phelps 1,008
Dawson 1,975

a) Compute and interpret the mean.
b) Compute the range.
c) Compute the variance.
d) Compute the standard deviation.
e) Compute the coefficient of variation for the scores.
f) A sample of counties in Nebraska from 2010 provided a sample mean of 1,331
businesses and a sample standard deviation of 1,151 businesses. What comparisons can
you make between the number of businesses/county in 2016 and 2010 based on these
descriptive statistics?

Expert Solution

Mean= sum of all observation/total number of observations Mean : 1924.8888888889 this is the average or mean business of 9 counties which is greater than the the average number of businesses per county in Nebraska.
Variance : 2566088.0987654

Standard deviation= sqrt(2566088.0987654)= 1601.90

Range= maximum- minimum= 3992-279= 3713

Coefficient of variation= S*100/xbar= 1601.90*100/1924.89= 83.22% The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average). Here in this case, the expression “The standard deviation is 83.22% of the mean.

f) Mean business in 2010 is 1331 which is less than the average business done in 2016 in 9 countoco

Sample standard deviation in 2010 is 1151 is also less than the standard deviation in 2016 of 9 counties

CV= 1151*100/1331= 86.47% but coefficient of variation of 2010 bussinbu is greater than the coefficient of variation of 2016 business.

orchestra answered 2 years ago

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