Question

find the mean, median, and mode for the set of numbers. if necessary, round the mean to one decimal place. 12, 15, 20, 11, 22. find the mean. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mean is (type a whole number or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.) b. there is no mean. find the median. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the median is (type a whole number or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.) b. there is no median. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode is (type a whole number or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.) b. there is no mode.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a set of numbers $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $x_1 = 12,x_2=15,x_3 = 20,x_4=11,x_5 = 22$ and $n = 5$. So, $\bar{x}=\frac{12 + 15+20+11+22}{5}=\frac{80}{5}=16$.

Step2: Find the median

First, order the data - set: $11,12,15,20,22$. Since $n = 5$ (an odd number), the median is the middle - value. The middle - value of a set with $n = 5$ ordered values is the third value. So the median is $15$.

Step3: Determine the mode

The mode is the number that appears most frequently in the data - set. In the set $\{12,15,20,11,22\}$, each number appears only once. So there is no mode.

Answer:

Mean: A. The mean is 16
Median: A. The median is 15
Mode: B. There is no mode