Question

listed below are the ages of 11 players randomly selected from the roster of a championship sports team. find the (a) mean, (b) median, (c) mode, and (d) mid - range and then (e)
b. find the median.
the median age is 28 years.
(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) 23,28,30 year(s)
(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.
the midrange is 32 years.
(type an integer or a decimal rounded to one decimal place as needed.)
e. how are the resulting statistics fundamentally different from those calculated from the jersey numbers of the same 11 players?
the jersey numbers are data at the ordinal level of measurement, but the ages are data at the nominal level of measurement, so only the jersey statistics are meaningful

Explanation:

Step1: Recall mid - range formula

The mid - range is calculated as $\frac{\text{Maximum value}+\text{Minimum value}}{2}$.

Step2: Identify maximum and minimum values

Let's assume we have the data set of ages. From the problem, we know the mid - range is already given as 32 years. But if we were to calculate it from scratch, we would first find the maximum and minimum values in the data set of 11 players' ages. Let the maximum age be $M$ and the minimum age be $m$. Then the mid - range $MR=\frac{M + m}{2}$.

Answer:

The mid - range is calculated as the average of the maximum and minimum values in the data set. If we assume the maximum age is $M$ and the minimum age is $m$, the mid - range formula is $\frac{M + m}{2}$. Since the mid - range is given as 32 years, it implies that for the data set of ages of the 11 players, $\frac{M + m}{2}=32$. Without the full data set of ages, we can't calculate $M$ and $m$ explicitly, but the concept remains the same. If we had the data set, say the ages are $x_1,x_2,\cdots,x_{11}$, we would first find $\max(x_1,x_2,\cdots,x_{11})$ and $\min(x_1,x_2,\cdots,x_{11})$ and then apply the formula. However, based on the information provided, we know the mid - range value is 32 years.