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 peas. listed below are the phenotype codes where 1 = smooth - yellow, 2 = smooth - green, 3 = wrinkled - yellow, 4 = wrinkled - green. do the results make sense? 2 3 1 4 4 1 2 2 4 2 1 1 1 1 (type an integer or a decimal. do not round. use a comma to separate answers as needed.) b. there is no mode. (d) the midrange of the phenotype codes is 2.5 (type an integer or decimal rounded to one decimal place as needed.) do the measures of center make sense? a. all the measures of center make sense since the data is numerical. b. only the mean, median, and midrange make sense since the data is nominal. c. only the mode makes sense since the data is nominal. d. only the mean, median, and mode make sense since the data is numerical.

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $2 + 3+1 + 4+4 + 1+2+2+4+2+1+1+1+1=26$. There are $n = 14$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{26}{14}\approx1.857143$.

Step2: Calculate the median

Arrange the data in ascending order: $1,1,1,1,1,2,2,2,2,2,3,4,4,4$. Since $n = 14$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The $\frac{14}{2}=7$th and $8$th values are $2$ and $2$, so the median $=\frac{2 + 2}{2}=2$.

Step3: Calculate the mode

The mode is the value that appears most frequently. The number $1$ appears $5$ times, the number $2$ appears $5$ times, the number $3$ appears $1$ time, and the number $4$ appears $3$ times. So the modes are $1,2$.

Step4: Calculate the mid - range

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

Step5: Determine if the measures of center make sense

The data represents phenotype codes which are nominal data (categories represented by numbers). Mean and median are not meaningful for nominal data as the numbers do not have a natural ordering or arithmetic meaning in this context. Only the mode makes sense as it tells us the most frequently occurring phenotype.

Answer:

(a) $1.857143$
(b) $2$
(c) $1,2$
(d) $2.5$
For the question "Do the measures of center make sense?": C. Only the mode makes sense since the data is nominal.