Questions: 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? 16, 54, 69, 39, 45, 81, 22, 65, 48, 66, 76

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?
16, 54, 69, 39, 45, 81, 22, 65, 48, 66, 76

Transcript text: 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? \[ \begin{array}{lllllllllll} 16 & 54 & 69 & 39 & 45 & 81 & 22 & 65 & 48 & 66 & 76 \end{array} \]

Solution

Solution Steps

Step 1: Mean Calculation

The mean (average) of the dataset is calculated using the formula: Mean = $\frac{\sum_{i=1}^{n} D_i}{n}$. For our dataset, the mean is 52.82.

Step 2: Median Calculation

The dataset has an odd number of elements, so the median is the middle number: Median = $D_{\frac{n+1}{2}}$. For our dataset, the median is 54.

Step 3: Mode Calculation

The dataset has no mode as each number appears only once.

Step 4: Midrange Calculation

The midrange of the dataset is calculated using the formula: Midrange = $\frac{\min(D) + \max(D)}2$. For our dataset, the midrange is 48.5.

Final Answer:

The dataset's mean is 52.82, median is 54, mode is No mode, and midrange is 48.5. These measures of central tendency and dispersion provide insights into the dataset's distribution, indicating how the data points are spread around the central value.

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