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 1equalssmooth-yellow, 2equalssmooth-green, 3equalswrinkled yellow, and 4 equalswrinkled-green.
1 1 4 1 3 1 3 3 2 2 2 3 1 2 2 2 2 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 standard deviation of the sample data is nothing. (Round to one decimal place as needed.)
B. The standard deviation of the sample data cannot be calculated. 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.
A. The variance of the sample data is nothing. (Round to one decimal place as needed.)
B. The variance of the sample data cannot be calculated.

Do the results makesense?
A. The measures of variation do not make sense because the standard deviation cannot be greater than the variance.
B. 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.
C. The measures of variation make sense because the data is numeric, so the spread between the values is meaningful.
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.

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

Step-by-step explanation:

Categories               X        x-x`      (x-x`)²

1                                 5         0          0

2                                10        5          25

3                                4         -1            1

4                                1           -4         16

                            ∑x= 20 ∑x-x` =0  ∑ (x-x`)²=42

Yes the range for these values can be obtained as range gives the idea of the spread of the values and is simply the difference between the largest and smallest value . The range of this data is 10-1= 9

The standard deviation is given by  √∑(x-x`)²/n

where x` is the mean and is calculated as = 20/4=5  

and n is the number of observations

S.D= √42/4 =√10.5= 3.24

And Variance is 10.5

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.