Question

reason and sense making in math
who is the greatest of all time?
below is a list of average points per season in the most recent 10 seasons for lebron james, kareem
abdul jabbar, and michael jordan. calculate the average (mean, median or mode) and compare the
players based on the averages you calculated. explain which type of average you chose and why it is the
best choice, then justify who is the best player based on your calculations. show all of your work.
lebron james\tkareem abdul jabbar\tmichael jordan
25.7\t10.1\t20.0
28.9\t14.6\t22.9
30.3\t17.5\t28.7
25.0\t23.4\t29.6
25.3\t22.0\t30.4
27.4\t21.5\t26.9
27.5\t21.8\t32.6
26.4\t23.9\t30.1
25.3\t26.2\t31.5
25.3\t24.8\t33.6
average points per
season

Explanation:

Step1: Calculate the mean for LeBron James

The formula for the mean is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For LeBron James, \(n = 10\), and the data points \(x=\{25.7,28.9,30.3,25.0,25.3,27.4,27.5,26.4,25.3,25.3\}\).

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The mean \(\bar{x}_{L}=\frac{267.1}{10}=26.71\)

Step2: Calculate the mean for Kareem Abdul - Jabbar

For Kareem Abdul - Jabbar, \(n = 10\), and the data points \(x = \{10.1,14.6,17.5,23.4,22.0,21.5,21.8,23.9,26.2,24.8\}\)

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The mean \(\bar{x}_{K}=\frac{205.8}{10}=20.58\)

Step3: Calculate the mean for Michael Jordan

For Michael Jordan, \(n = 10\), and the data points \(x=\{20.0,22.9,28.7,29.6,30.4,26.9,32.6,30.1,31.5,33.6\}\)

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LATEXBLOCK2
$$

The mean \(\bar{x}_{M}=\frac{286.3}{10}=28.63\)

Step4: Calculate the median for LeBron James

Sort the data: \(25.0,25.3,25.3,25.3,25.7,26.4,27.4,27.5,28.9,30.3\)
Since \(n = 10\) (even), the median \(M_{L}=\frac{25.7 + 26.4}{2}=26.05\)

Step5: Calculate the median for Kareem Abdul - Jabbar

Sort the data: \(10.1,14.6,17.5,21.5,21.8,22.0,23.4,23.9,24.8,26.2\)
Since \(n = 10\) (even), the median \(M_{K}=\frac{21.8+22.0}{2}=21.9\)

Step6: Calculate the median for Michael Jordan

Sort the data: \(20.0,22.9,26.9,28.7,29.6,30.1,30.4,31.5,32.6,33.6\)
Since \(n = 10\) (even), the median \(M_{M}=\frac{29.6 + 30.1}{2}=29.85\)

Step7: Calculate the mode for LeBron James

The mode is the most - frequent value. For LeBron James, the mode \(Mo_{L}=25.3\)

Step8: Calculate the mode for Kareem Abdul - Jabbar

There is no repeated value (all values occur once), so there is no mode (\(Mo_{K}=\text{None}\))

Step9: Calculate the mode for Michael Jordan

There is no repeated value (all values occur once), so there is no mode (\(Mo_{M}=\text{None}\))

Step10: Justify the choice of average

The mean is a good choice because it takes into account all the data points. The median is less affected by extreme values, but in a sports context, we want to consider all the seasons' performance. The mode is not useful here as most data sets have no mode or a mode that does not represent the overall performance well.

Answer:

• Mean of LeBron James: \(26.71\), Median: \(26.05\), Mode: \(25.3\)
• Mean of Kareem Abdul - Jabbar: \(20.58\), Median: \(21.9\), Mode: None
• Mean of Michael Jordan: \(28.63\), Median: \(29.85\), Mode: None

Since the mean is a comprehensive measure (using all data points), and \(\bar{x}_{M}(28.63)>\bar{x}_{L}(26.71)>\bar{x}_{K}(20.58)\), Michael Jordan has the highest mean. So, based on the mean (the best - chosen average for considering all - season performance), Michael Jordan is the best player among the three.