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) midrange and then​ (e) determine how the resulting statistics are fundamentally different from those calculated from the jersey numbers of the same 11 players.
use as reference Ages
41
20
31
32
34
26
23
24
23
31
24

Jersery Numbers
13
26
50
11
9
85
74
58
61
70
57
mean
median
mode
min
max
midrange
46.7
57
none
9
85
47
what is the mean age

To find the mean age of the 11 players, we need to sum all the ages and then divide by the number of players. Let's go step by step:

Given ages: 41, 20, 31, 32, 34, 26, 23, 24, 23, 31, 24

### Steps:

1. **Sum of the ages**: 
   \( 41 + 20 + 31 + 32 + 34 + 26 + 23 + 24 + 23 + 31 + 24 \)

2. **Number of players**: 11

3. **Mean**: 
   \[
   \text{Mean} = \frac{\text{Sum of the ages}}{\text{Number of players}}
   \]

Let's calculate the mean.The mean age of the 11 players is approximately **28.09 years**.

### Key Points on Fundamental Differences:

- **Ages**: Represent a quantitative measurement of time and are continuous. They have meaningful averages, medians, and modes. The mean age (28.09 years) is meaningful and represents the central tendency of the players' ages.
  
- **Jersey Numbers**: Are categorical or nominal data. Their averages, medians, and midranges are not meaningful in the same way because jersey numbers don't have an inherent numerical relationship or order. The statistics computed (mean, median, etc.) from jersey numbers don’t provide insights into the players themselves but are simply calculations on arbitrary labels.

Would you like to go through the other statistics like median, mode, and midrange? 

### Next Steps and Questions:
1. Would you like the calculation for the median of the ages?
2. Should I compute the mode of the ages?
3. Are you interested in the midrange for the ages?
4. Do you need clarification on why jersey numbers don’t have meaningful statistics?
5. Should I compute all statistics to compare the data sets in detail?

**Tip:** Always ensure you’re aware of whether your data is qualitative or quantitative when calculating statistics; this prevents the misinterpretation of meaningless results.

Explore the statistical analysis of player ages and jersey numbers from a championship sports team. Calculate the mean, median, mode, and midrange of ages to understand central tendencies. Compare these results with statistics from jersey numbers to understand the differences in quantitative versus categorical data analysis.

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