Math Problem Statement

In this stem-and-leaf plot, the stems represent tens and the leaves represent ones. Find the median and range of the data.

Solution

The stem-and-leaf plot in the image shows the data, where the stems represent the tens digits, and the leaves represent the ones digits. Let's break down the plot to extract the numbers:

  • Stem 2: Leaves 6, 8, 9 → 26, 28, 29
  • Stem 3: Leaves 1, 1 → 31, 31
  • Stem 4: Leaves 2, 3, 3, 5 → 42, 43, 43, 45
  • Stem 6: Leaves 4, 5, 5, 5, 6, 7, 8 → 64, 65, 65, 65, 66, 67, 68
  • Stem 7: Leaves 2, 2, 2, 2, 3, 3, 4, 9 → 72, 72, 72, 72, 73, 73, 74, 79
  • Stem 8: Leaves 0, 1, 7, 7, 8 → 80, 81, 87, 87, 88
  • Stem 9: Leaves 6, 6 → 96, 96

Now we will list the numbers in order: 26,28,29,31,31,42,43,43,45,64,65,65,65,66,67,68,72,72,72,72,73,73,74,79,80,81,87,87,88,96,9626, 28, 29, 31, 31, 42, 43, 43, 45, 64, 65, 65, 65, 66, 67, 68, 72, 72, 72, 72, 73, 73, 74, 79, 80, 81, 87, 87, 88, 96, 96

Median:

The total number of values is 31, which is odd. The median is the middle number, which is the 16th value in the ordered list.

Median=66\text{Median} = 66

Range:

The range is the difference between the highest and lowest numbers.

Range=9626=70\text{Range} = 96 - 26 = 70

Thus:

  • Median = 66
  • Range = 70

Would you like more details on how to interpret stem-and-leaf plots, or any questions on the steps?

Here are 5 related questions:

  1. How do you find the mode of a stem-and-leaf plot?
  2. Can you explain how quartiles can be determined from a stem-and-leaf plot?
  3. What are the advantages of using a stem-and-leaf plot over a histogram?
  4. How would you find the interquartile range (IQR) from the given data?
  5. What does the shape of the data distribution tell us about the dataset?

Tip: In stem-and-leaf plots, always check for duplicate values when calculating the median or any other statistical measure.

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Math Problem Analysis

Mathematical Concepts

Statistics
Stem-and-Leaf Plot
Median
Range

Formulas

Median: The middle value in an ordered dataset.
Range: The difference between the maximum and minimum values.

Theorems

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Suitable Grade Level

Grades 6-8