Question

Find the​ range, variance, and standard deviation for the given sample​ data, if possible. If the measures of variation can be obtained for these​ values, do the results make​ sense?

Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype​ codes, where 1=​smooth-yellow, 2=​smooth-green, 3=wrinkled yellow, and 4=​wrinkled-green.

2 1 3 2 3 1 4 3 2 2 2 3 2 2 2 2 1 2 2 2

1. Can the range of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice.

2. Can the standard deviation of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The standard deviation of the sample data is

3.Can the variance of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The variance of the sample data is

4. Do the results make​ sense?

A. The measures of variation do not make sense because the standard deviation cannot be greater than the variance.

B. The measures of variation make sense because the data is​ numeric, so the spread between the values is meaningful.

C. While the measures of variation can be​ found, they do not make sense because the data are​ nominal; they​ don't measure or count anything.

D. It makes sense that the measures of variation cannot be calculated because there is not a large enough sample size to calculate the measures of variation.

Answer 1

1. Can the range of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice.

Range= 3

2. Can the standard deviation of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The standard deviation of the sample data is 0.75

3.Can the variance of the sample data be obtained for these​ values? Choose the correct answer below​ and, if​ necessary, fill in the answer box within your choice. The variance of the sample data is 0.56

4. Do the results make​ sense?

While the measures of variation can be​ found, they do not make sense because the data are​ nominal; they​ don't measure or count anything.