Math Problem Statement

A college basketball player scored the following points in the 37 games he played his senior year: Stem-and-leaf of points n = 37 Leaf Unit = 1.0

1 33 1 66 2 1233444 2 5555666789 3 0222233444 3 89 4 23 4 7 5 2

His median score is ____________ points.

Solution

To determine the median score of the player's points, we need to follow these steps:

Step 1: Arrange the Data in Ascending Order

The stem-and-leaf plot already provides the data sorted. Let's list out the points explicitly:

  • 13, 16,
  • 21, 22, 23, 24, 24, 24,
  • 25, 25, 25, 25, 26, 26, 26, 27, 28, 29,
  • 30, 30, 30, 32, 32, 33, 34, 34, 34,
  • 38, 39,
  • 42, 43,
  • 47,

So, the ordered list is: 13, 16, 21, 22, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 27, 28, 29, 30, 30, 30, 32, 32, 33, 34, 34, 34, 38, 39, 42, 43, 47, 52

Step 2: Find the Median Position

The median is the middle value when the data is sorted. Since there are 37 scores, the median is at position:

Median Position=n+12=37+12=19\text{Median Position} = \frac{n + 1}{2} = \frac{37 + 1}{2} = 19

Thus, the 19th value in the sorted list is the median.

Step 3: Identify the 19th Value

From the ordered list, counting to the 19th value gives:

30

Final Answer:

The median score is 30 points.


Would you like an explanation of finding medians in other scenarios? 😊

5 Related Questions:

  1. What is the mode of the data set?
  2. How do you calculate the mean of the scores from the given data?
  3. What percentage of the games had a score above the median?
  4. How do outliers impact measures of central tendency like the mean or median?
  5. What is the range of scores in the data set?

Tip:

Always double-check whether the number of data points is odd or even when finding the median! For even counts, take the average of the two middle values.

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Math Problem Analysis

Mathematical Concepts

Statistics
Median
Data Interpretation

Formulas

Median Position = (n + 1) / 2

Theorems

Concept of Median in Statistics

Suitable Grade Level

Grades 9-12