Math Problem Statement

Use a stem and leaf display to organize the following distribution of scores: 36, 47, 14, 19, 65, 52, 47, 42, 11, 25, 28, 39, 32, 34, 58, 57, 22, 49, 22, 16, 33, 37, 23, 55, 44. Use six stems with each stem corresponding to a 10-point interval.

Solution

To create a stem-and-leaf display, we will organize the scores by separating the tens place (stem) from the units place (leaf). The stems represent the tens interval, and each leaf represents the unit digit of the scores.

Given Scores:

  • 36, 47, 14, 19, 65
  • 52, 47, 42, 11, 25
  • 28, 39, 32, 34, 58
  • 57, 22, 49, 22, 16
  • 33, 37, 23, 55, 44

Step 1: Identifying Stems

The problem asks for 6 stems with each stem corresponding to a 10-point interval. The intervals would be:

  • 10–19
  • 20–29
  • 30–39
  • 40–49
  • 50–59
  • 60–69

Step 2: Organizing the Leaves

Now we place each score under its appropriate stem (tens digit).

StemLeaves
11, 4, 6, 9
22, 2, 3, 5, 8
32, 3, 4, 6, 7, 9
42, 4, 7, 7, 9
52, 5, 7, 8
65

Final Stem-and-Leaf Plot:

1 | 1 4 6 9
2 | 2 2 3 5 8
3 | 2 3 4 6 7 9
4 | 2 4 7 7 9
5 | 2 5 7 8
6 | 5

This stem-and-leaf plot is now organized as requested, where each stem represents a 10-point interval.

Would you like further clarification or details on how this was done?


Here are five related questions:

  1. How would the stem-and-leaf plot change if the scores ranged up to 100?
  2. Can a stem-and-leaf plot handle decimal numbers? How?
  3. How would you calculate the median from a stem-and-leaf plot?
  4. What is the range of the given data set?
  5. How can stem-and-leaf plots help in identifying outliers?

Tip: A stem-and-leaf plot is a great way to maintain the original data while visualizing its distribution.

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Math Problem Analysis

Mathematical Concepts

Data Visualization
Stem-and-Leaf Plot

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8