Math Problem Statement

Find the median and range from the stem-and-leaf plot.

Solution

The provided image shows a stem-and-leaf plot where the stems represent tens and the leaves represent ones. We are asked to find the median and the range of the data.

Extracting the data from the stem-and-leaf plot:

  • 10, 11, 13, 13, 14
  • 21, 21, 25, 27
  • 48, 49, 49, 49
  • 50, 51, 52, 56
  • 63, 63, 64
  • 86, 87, 87, 89
  • 93, 94, 94, 98

So the complete list of numbers is: 10,11,13,13,14,21,21,25,27,48,49,49,49,50,51,52,56,63,63,64,86,87,87,89,93,94,94,9810, 11, 13, 13, 14, 21, 21, 25, 27, 48, 49, 49, 49, 50, 51, 52, 56, 63, 63, 64, 86, 87, 87, 89, 93, 94, 94, 98

Step 1: Finding the Median

To find the median, we first arrange the data (which is already arranged) and count the total number of values. There are 28 values, so the median will be the average of the 14th and 15th numbers in the list:

  • The 14th number is 49.
  • The 15th number is 50.

Thus, the median is: Median=49+502=49.5\text{Median} = \frac{49 + 50}{2} = 49.5

Step 2: Finding the Range

The range is the difference between the highest and lowest values in the data set:

  • Highest value: 98
  • Lowest value: 10

Thus, the range is: Range=9810=88\text{Range} = 98 - 10 = 88

Final Answers:

  • Median = 49.5
  • Range = 88

Would you like further details or explanations on any part of this process? Here are five related questions to explore:

  1. How do you calculate the mode from a stem-and-leaf plot?
  2. Can a stem-and-leaf plot display decimal values, and how would that affect calculations?
  3. What is the significance of outliers in calculating the range?
  4. How do you find the quartiles in a stem-and-leaf plot?
  5. Can the median ever be the same as the mean in a data set? Why or why not?

Tip: When calculating the median from an even set of numbers, always average the two middle values to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Statistics
Stem-and-leaf plots
Median
Range

Formulas

Median = Average of the two middle numbers if even set
Range = Largest value - Smallest value

Theorems

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Suitable Grade Level

Grades 6-8