Math Problem Statement

A college basketball player scored the following points in 37 games. Calculate the median score using the given stem-and-leaf plot.

Solution

It seems you've uploaded an image. I'll first analyze the content of the image and extract the relevant mathematical information to assist you with it. Please give me a moment to review it. PIL import Image

Open the uploaded image to inspect its contents

image_path = '/mnt/data/1733701730856sbkzfsjx.jpg' img = Image.open(image_path)

Display the image to understand its contents

img.show()I've displayed the image for review. Now, I will extract the mathematical content and provide a solution. Let me proceed with analyzing the image. pytesseract

Use OCR (Optical Character Recognition) to extract text from the image

extracted_text = pytesseract.image_to_string(img)

Display the extracted text for review

extracted_textThe image contains data about a college basketball player's performance in 37 games, with a stem-and-leaf plot showing the distribution of points scored. Here’s the breakdown:

  • The data is presented in a stem-and-leaf plot format where:
    • "Stem" represents the tens digit, and
    • "Leaf" represents the ones digit (with each leaf unit being 1 point).

The stem-and-leaf data is as follows:

  • 33 (representing 33 points)
  • 66 (representing 66 points)
  • 1233444 (representing 12, 13, 14, 14 points)
  • 5555666789 (representing 5, 5, 5, 6, 6, 6, 7, 8, 9 points)
  • 0222233444 (representing 0, 2, 2, 2, 3, 3, 4, 4 points)
  • 89 (representing 8, 9 points)

The question asks for the median score of the player based on this data.

Let's now calculate the median from this stem-and-leaf plot.

To Find the Median:

  • We need to list all the data points in numerical order.
  • Then, find the middle value of the ordered data.

Let me calculate the median for you. numpy as np

Reconstruct the full data from the stem-and-leaf plot

data = [ 33, 66, 12, 13, 14, 14, 5, 5, 5, 6, 6, 6, 7, 8, 9, 0, 2, 2, 2, 3, 3, 4, 4, 89 ]

Sort the data

data_sorted = sorted(data)

Find the median

median_index = len(data_sorted) // 2

If the number of data points is odd, the median is the middle element

If even, it's the average of the two middle elements

if len(data_sorted) % 2 == 1: median = data_sorted[median_index] else: median = (data_sorted[median_index - 1] + data_sorted[median_index]) / 2

median, data_sortedThe median score for the player is 6.0 points.

Here is the full sorted list of points scored:

[0, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 12, 13, 14, 14, 33, 66, 89]

Since there are 24 data points (an even number), the median is the average of the two middle numbers: 6 and 6, resulting in a median of 6.

Do you have any further questions or would you like additional details about how this was calculated?

Here are 5 related questions that might interest you:

  1. How do you interpret a stem-and-leaf plot?
  2. How does the median differ from the mean and mode?
  3. What are some other ways to calculate the central tendency of data?
  4. How do you handle outliers in data when calculating the median?
  5. Can you calculate the range or standard deviation for this dataset?

Tip: When working with stem-and-leaf plots, always remember that the "leaf unit" tells you how to interpret the numbers. In this case, each leaf represents 1 point.

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Math Problem Analysis

Mathematical Concepts

Statistics
Median
Stem-and-leaf plots

Formulas

Median formula: Middle value in a sorted data set

Theorems

Basic properties of median

Suitable Grade Level

Grades 6-9