Problem 20BSC

In Exercise, find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. 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 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4 = wrinkled-green. 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

Answer:

Step 1 of 1

(a) The "Mean" is computed by adding all of the numbers in the data together and dividing by the number elements contained in the data set.

Mean = = 1.88

(b) The "Median" of a data set is dependant on whether the number of elements in the data set is odd or even. First reorder the data set from the smallest to the largest then if the number of elements are odd, then the Median is the element in the middle of the data set. If the number of elements are even, then the Median is the average of the two middle terms.

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 |

Median = 2

(c) The "Mode" for a data set is the element that occurs the most often. It is not uncommon for a data set to have more than one mode. This happens when two or more elements occur with equal frequency in the data set. A data set with two modes is called bimodal. A data set with three modes is called trimodal.

Since there is no repeated terms in the data. Hence there is no mode.

(d) In statistics, the mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as

Mid range = 2.5

Yes, the measures of center be obtained for these values and they make sense. It means that most of the experimental results show smooth green.