find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given…

find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. what do the results tell us? 20 39 14 81 15 34 78 9 29 85 28 \n\n a. find the mean. the mean is 39.3. (type an integer or a decimal rounded to one decimal place as needed.) \n\n b. find the median. the median is 29. (type an integer or a decimal rounded to one decimal place as needed.) \n\n c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. \n\n a. the mode(s) is(are) \n (type an integer or a decimal. do not round. use a comma to separate answers as needed.) \n\n b. there is no mode.

find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. what do the results tell us? 20 39 14 81 15 34 78 9 29 85 28 \n\n a. find the mean. the mean is 39.3. (type an integer or a decimal rounded to one decimal place as needed.) \n\n b. find the median. the median is 29. (type an integer or a decimal rounded to one decimal place as needed.) \n\n c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. \n\n a. the mode(s) is(are) \n (type an integer or a decimal. do not round. use a comma to separate answers as needed.) \n\n b. there is no mode.

Answer

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 11$, and $\sum_{i=1}^{11}x_{i}=20 + 39+14 + 81+15 + 34+78+9+29+85+28=432$. So, $\bar{x}=\frac{432}{11}\approx39.3$.

Step2: Calculate the median

First, arrange the data in ascending order: $9,14,15,20,28,29,34,39,78,81,85$. Since $n = 11$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+1}{2}=6$ - th value, which is $29$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. In the data - set $20,39,14,81,15,34,78,9,29,85,28$, each value appears only once. So, there is no mode.

Step4: Calculate the mid - range

The mid - range is calculated as $\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is $9$ and the maximum value is $85$. So, the mid - range $=\frac{9 + 85}{2}=\frac{94}{2}=47$.

Answer:

a. The mean is $39.3$. b. The median is $29$. c. B. There is no mode. d. The mid - range is $47$. The results tell us that the average jersey number (mean) is approximately $39.3$, the middle - valued jersey number (median) is $29$, there is no frequently occurring jersey number (no mode), and the mid - range of the jersey numbers is $47$. These measures give us an idea about the central tendency and spread (in a basic sense with the mid - range) of the jersey numbers of the selected players.