Problem 20BSC
In Exercise, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 32 where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Phenotypes of Peas 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 = smoothyellow, 2 = smoothgreen, 3 = wrinkledyellow, and 4 = wrinkledgreen. Can the measures of center be obtained for these values? Do the results make sense?
2 1 1 1 1 1 1 4 1 2 2 1 2 3 3 2 3 1 3 1 3 1 3 2 2
Problem 20BSC
Answer:
Step1 of 3:
We have 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 = smoothyellow, 2 = smoothgreen, 3 = wrinkledyellow, and 4 = wrinkledgreen.
2 
1 
1 
1 
1 
1 
1 
4 
1 
2 
2 
1 
2 
3 
3 
2 
3 
1 
3 
1 
3 
1 
3 
2 
2 
Step2 of 3:
We need to find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 32 where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Step3 of 3:
1).Range can be calculated by using the formula Range = maximum value  minimum value
The given data in Ascending order
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 
4 
Here,
Maximum value = 4
Minimum value = 1
Now,
Range = maximum value  minimum value
= 4  1
= 3
Therefore, Range = 3
2).consider,
x 
(x  )2 

1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 
1.88 
0.7744 
1 