Math Problem Statement

Find the following for the data in the stemplot below: a. mean, b. median, c. mode, d. midrange.

Solution

The image contains a question that requires statistical analysis based on the data in a stem-and-leaf plot. Let's address the specific tasks:

Data:

  • 0 | 7888
  • 1 | 0349
  • 2 | 379
  • 3 | 002
  • 4 | 5

These numbers correspond to the following values:

  • 7, 8, 8, 8
  • 10, 13, 14, 19
  • 23, 27, 29
  • 30, 30, 32
  • 45

Let's compute the required values:

a. Mean

The mean is the sum of all values divided by the number of values.

b. Median

The median is the middle value when the numbers are arranged in ascending order.

c. Mode

The mode is the value(s) that occur most frequently.

d. Midrange

The midrange is the average of the smallest and largest values in the data set.

Let me calculate each of these for you.Here are the statistical calculations based on the data provided:

  1. Mean: 20.220.2
  2. Median: 1919
  3. Mode: 88 (it occurs most frequently)
  4. Midrange: 2626 (calculated as the average of the smallest value 77 and largest value 4545)

Would you like more details or have any questions?

Here are five related questions to expand on this topic:

  1. How do changes in the data affect the mean and median differently?
  2. Can a data set have more than one mode? If so, when?
  3. Why is the midrange not commonly used as a measure of central tendency?
  4. How does the distribution of data affect the choice of mean, median, or mode for analysis?
  5. What is the relationship between range and midrange?

Tip: The median is a robust measure of central tendency because it is less affected by outliers than the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean = (sum of all data points) / (number of data points)
Median: the middle value when data points are ordered
Mode: the most frequent data point
Midrange = (smallest value + largest value) / 2

Theorems

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Suitable Grade Level

Grades 6-8