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? 4 4 4 3 4 3 1 3 4 4 2 1 1 3 (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 mode makes sense since the data is nominal. c. only the mean, median, and mode make sense since the data is numerical. d. only the mean, median, and midrange make sense since the data is nominal.

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $4 + 4+4 + 3+4+3+1+3+4+4+2+1+1+3=40$. There are $n = 14$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{40}{14}\approx2.86$.

Step2: Calculate the median

Arrange the data in ascending order: $1,1,1,2,3,3,3,3,4,4,4,4,4,4$. 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 7th value is $3$ and the 8th value is $3$, so the median $M=\frac{3 + 3}{2}=3$.

Step3: Calculate 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 $4$.

Step4: Calculate the mid - range

The mid - range is calculated as $\text{Mid - range}=\frac{\text{Min}+\text{Max}}{2}$. 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 values ($1 =$ smooth - yellow, $2 =$ smooth - green, $3 =$ wrinkled - yellow, $4 =$ wrinkled - green) are nominal data. Nominal data are categorical and do not have a natural ordering or numerical meaning in the arithmetic sense. Only the mode makes sense for nominal data.

Answer:

(a) $2.86$
(b) $3$
(c) $4$
(d) $2.5$
Do the measures of center make sense? B. Only the mode makes sense since the data is nominal.