Math Problem Statement

The following refer to the following data set: 52.8, 57.2, 73.1, 68.5, 41.1, 38.7, 73.1, 40.8, 59, 73.1. What is the arithmetic mean, median, and mode of this data set?

Solution

Here are the results for the given data set:

  • Mean (arithmetic average) = 57.74
  • Median (middle value) = 58.1
  • Mode (most frequent value) = 73.1

Would you like more details or explanations on these calculations?

Here are some related questions to consider:

  1. How would the mean change if a new value is added to the dataset?
  2. What if there are two modes in the dataset, how do we handle that?
  3. How do you calculate the range of the dataset?
  4. What is the difference between median and mode in terms of their real-life applications?
  5. How would removing an outlier affect the mean and median?

Tip: The mean is sensitive to outliers, whereas the median is more robust when there are extreme values in the data.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Mean
Median
Mode

Formulas

Mean = (sum of all data points) / (number of data points)
Median = middle value of an ordered data set
Mode = most frequent value in a data set

Theorems

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Suitable Grade Level

Grades 6-8