Question

In: Math

The standard deviation alone does not measure relative variation. For example, a standard deviation of $1...

The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/ x ). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.

Sample 1 8.2 7.3 7.4 8.6 7.4
8.2 8.6 7.5 7.5 7.1
Sample 2 51.8 51.2 51.9 51.6 52.7
47 50.4 50.3 48.7 48.2

(a) For each of the given samples, calculate the mean and the standard deviation. (Round all intermediate calculations and answers to five decimal places.)

For sample 1
Mean
Standard deviation
For sample 2
Mean
Standard deviation


(b) Compute the coefficient of variation for each sample. (Round all answers to two decimal places.)

CV1
CV2

Solutions

Expert Solution

Coefficient of variation is a relative measure of dispersion. The smaller the coefficient of variation, the better efficient the data is. We can see that the second sample has less coefficient of variation than sample 1. The mean and standard deviations of two samples are shown with all necessary steps and calculations. I hope you can understand this solution.


Related Solutions

The coefficient of variation is a better measure of stand-alone risk than standard deviation because it...
The coefficient of variation is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit; it is calculated as the -Select-correlation coefficientrisk premiumstandard deviationCorrect 5 of Item 1 divided by the expected return. The coefficient of variation shows the risk per unit of return, so it provides a more meaningful risk measure when the expected returns on two alternatives are not -Select-identicaldifferentcorrelatedCorrect 6 of Item 1. The Sharpe ratio compares the...
Provide an example of how standard deviation is used to measure sports statistics (other than the...
Provide an example of how standard deviation is used to measure sports statistics (other than the examples in the book). Feel free to use an example outside of sports. (econ of sports)
determine (1) % Fe in unknown sample (2)average % Fe (3)standard deviation (4)relative standard deviation For...
determine (1) % Fe in unknown sample (2)average % Fe (3)standard deviation (4)relative standard deviation For gravimetric determination of Iron as Fe2O3, how do I calculate? weighed sample of unknown containing Fe to produce ~0.3g of Fe2O3 (~0.6 - 1 g of unkonwn) I got 0.75g from unknow sample. I got 0.05g from Fe2O3 collected from unknow.
Discuss the standard deviation of a risky asset's return. What does it measure? Also discuss the...
Discuss the standard deviation of a risky asset's return. What does it measure? Also discuss the 95% confidence interval of a risky asset's return and how it's related to the asset's standard deviation
Compare and contrast: (1) Describe the meaning of beta, standard deviation and coefficient of variation. (2)...
Compare and contrast: (1) Describe the meaning of beta, standard deviation and coefficient of variation. (2) How each of them can be used to stock investment? For example, how you select an investment using each of these three measures? (this is an open question, the answer will be graded based on student's understanding on each concept)
Q1: Estimate the absolute standard deviation and the coefficient of variation for the results of the...
Q1: Estimate the absolute standard deviation and the coefficient of variation for the results of the following calculations. Round to the correct number of significant figures. The numbers in parenthesis are absolute standard deviations. y =5.75(±0.03) + 0.833(±0.001) – 8.021(±0.001) = -1.4381 y =18.97(±0.04) + .0025(±0.0001) +2.29(± .08)= 21.2625 y =66.2(±.3) x 1.13(±.02) x10-17 = 7.4806x10-16 y =251(±1) x 860(±2) / 1.673(±.006) = 129025.70 y = [157(±6) - 59(±3)] / [1220(±1) + 77(±8)] = 7.5559x10-2 y = 1.97(±.01) / 243(±3)...
Calculate the range, interquartile range, variance, standard deviation and coefficient of variation.
A sample has data values 27, 25, 20, 15, 30, 34, 28, 25. Calculate the range, interquartile range, variance, standard deviation and coefficient of variation.
Concept-Discussion 1 - Explain why the standard deviation would likely not be a reliable measure of...
Concept-Discussion 1 - Explain why the standard deviation would likely not be a reliable measure of variability for a distribution of data that includes at least one extreme outlier. Concept-Discussion 2 - Suppose that you collect a random sample of 250 salaries for the salespersons employed by a large PC manufacturer. Furthermore, assume that you find that two of these salaries are considerably higher than the others in the sample. Before analyzing this data set, should you delete the unusual...
Standard deviation is a measure of central tendency that is the difference between the highest and...
Standard deviation is a measure of central tendency that is the difference between the highest and lowest scores. True or False?
Calculate the standard deviation and coefficient of variation for each data set below, be sure to...
Calculate the standard deviation and coefficient of variation for each data set below, be sure to attach an Excel file to show the work. Explain which of the two mentioned measures can more accurately specify which of these two data sets has more variability or dispersion in their data values, and why. Data set 1= 11,12,13,14,15,16,17,18,19,20 Data set 2= 8,9,28,29,5,4,1,3,2,10
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT