Math Problem Statement

60 students were surveyed about how many nights in a week they work on homework problems in their MAT142 class. What is the mean and median number of days of homework?

Solution

To help you calculate the median number of days of homework, let's walk through the steps.

  1. Organize the data in ascending order: We need to first collect all the numbers from the table and sort them.

    Here are the numbers from the table:

    3, 1, 7, 5, 6, 6, 2, 6, 3, 2,
    4, 6, 3, 6, 5, 4, 3, 3, 4, 3,
    4, 4, 7, 2, 1, 2, 7, 1, 3, 5,
    1, 3, 1, 6, 3, 1, 6, 3, 1, 6,
    5, 5, 6, 6, 1, 2, 3, 2, 1, 3,
    5, 3, 1, 1, 1, 1, 1, 1, 3, 4
    
  2. Sort the data: After sorting the data in ascending order:

    1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    2, 2, 2, 2, 2, 3, 3, 3, 3, 3,
    3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
    4, 4, 5, 5, 5, 5, 5, 6, 6, 6,
    6, 6, 6, 6, 6, 6, 7, 7
    
  3. Identify the median: Since there are 60 values, the median is the average of the 30th and 31st values.

    • The 30th value is 4.
    • The 31st value is also 4.

    Therefore, the median is: 4+42=4\frac{4 + 4}{2} = 4

Thus, the median number of days of homework is 4.00.

Let me know if you'd like any more details or clarifications!

Here are five related questions to expand on the topic:

  1. How do you calculate the mode for this dataset?
  2. What is the range of the number of homework days?
  3. How would you compute the variance or standard deviation for this dataset?
  4. How does the median differ from the mean in terms of data analysis?
  5. Could you calculate the quartiles for this dataset?

Tip: When calculating medians, always sort the data first and identify the middle position based on whether you have an odd or even number of data points.

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median

Formulas

Mean = (sum of all data points) / (number of data points)
Median = middle value of sorted data set

Theorems

Median Theorem
Arithmetic Mean Theorem

Suitable Grade Level

Grades 9-12