Problem

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? $\begin{array}{llllllllllll}47 & 86 & 43 & 8 & 26 & 9 & 99 & 17 & 95 & 35 & 55 & \square\end{array}$ a. Find the mean. The mean is (Type an integer or a decimal rounded to one decimal place as needed.) b. Find the median. The median is (Type an integer or a decimal rounded to one decimal place as needed.) c. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode(s) is(are) (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode. d. Find the midrange.

Solution

Step 1 :First, we need to calculate the mean, which is the sum of all the numbers divided by the count of numbers. In this case, the mean is \(\frac{47 + 86 + 43 + 8 + 26 + 9 + 99 + 17 + 95 + 35 + 55}{11} = 47.27272727272727\).

Step 2 :Next, we find the median, which is the middle number in a sorted list of numbers. If the list has an even number of observations, the median will be the average of the two middle numbers. In this case, the median is 43.

Step 3 :Then, we find the mode, which is the number that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. In this case, there is no mode.

Step 4 :Finally, we find the midrange, which is the average of the maximum and minimum numbers in the data set. In this case, the midrange is \(\frac{99 + 8}{2} = 53.5\).

Step 5 :So, the mean is \(\boxed{47.3}\) (rounded to one decimal place as needed), the median is \(\boxed{43}\), there is no mode, and the midrange is \(\boxed{53.5}\).

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