Question

find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. an experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. listed below are the phenotype codes where 1 = smooth - yellow, 2 = smooth - green, 3 = wrinkled - yellow, and 4 = wrinkled - green. do the results make sense? 4 4 4 3 4 3 1 3 4 4 2 1 1 3 (a) the mean phenotype code is (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Calculate sum of data

Sum all the phenotype - codes: \(4 + 4+4 + 3+4 + 3+1+3+4+4+2+1+1+3=41\)

Step2: Determine number of data points

Count the number of phenotype - codes. There are \(n = 14\) data points.

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\text{Sum of data}}{\text{Number of data points}}=\frac{41}{14}\approx2.9\)

Step4: Arrange data in ascending order

\(1,1,1,2,3,3,3,3,4,4,4,4,4,4\)

Step5: Calculate the median

Since \(n = 14\) (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered data values. \(\frac{n}{2}=7\) and \(\frac{n}{2}+1 = 8\). The 7th value is \(3\) and the 8th value is \(3\), so the median \(\text{Median}=\frac{3 + 3}{2}=3\)

Step6: Find the mode

The mode is the value that appears most frequently. The number \(4\) appears \(6\) times, more frequently than any other number, so the mode is \(4\)

Step7: Calculate the mid - range

The mid - range is \(\frac{\text{Minimum value}+\text{Maximum value}}{2}\). The minimum value is \(1\) and the maximum value is \(4\), so the mid - range \(=\frac{1 + 4}{2}=2.5\)

The results for mean, median, mode and mid - range are valid statistical measures for this data set. However, these phenotype codes are categorical data that have been numerically coded. While the calculations are correct from a statistical perspective, the mean and mid - range may not have a direct biological interpretation as these codes are not truly numerical in a quantitative sense.

Answer:

(a) \(2.9\)
(b) \(3\)
(c) \(4\)
(d) \(2.5\)