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 2 2 1 3 3 4 2 2 2 2 1 2 2 2 3 1 2 2 2
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.
a. the range of the sample data is 3. (type an integer or a decimal. do not round.)
b. the range of the sample data cannot be calculated.
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.
a. the standard deviation of the sample data is . (round to one decimal place as needed.)
b. the standard deviation of the sample data cannot be calculated.

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum

Step2: Identify max and min

The given data set is 2, 2, 2, 1, 3, 3, 4, 2, 2, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2. The maximum value is 4 and the minimum value is 1.

Step3: Calculate range

Range = 4 - 1 = 3

Step4: Analyze standard - deviation calculation

The phenotype codes are categorical data (representing different phenotypes) that have been numerically coded for convenience. Standard deviation is a measure of dispersion for numerical data that has a meaningful order and arithmetic operations make sense. Here, the numbers are just codes for categories, and arithmetic operations like addition, subtraction on them do not have a real - world quantitative meaning. So, the standard deviation cannot be calculated.

Answer:

A. The range of the sample data is 3
B. The standard deviation of the sample data cannot be calculated