Math Problem Statement

A survey of 10 adults employed full-time was taken. Here are their reported numbers of hours worked per week: 43, 58, 36, 57, 55, 46, 48, 50, 41, 59. What is the mean, median, and mode of this data set?

Solution

Here are the answers to the questions based on the data provided:

(a) The mean of the data set is 49.349.3.

(b) The median of the data set is 49.049.0.

(c) The data set has zero modes because all values are unique and occur only once.

Would you like any further details or clarifications?

Here are five related questions to expand your understanding:

  1. What is the relationship between mean, median, and mode in a symmetrical data set?
  2. How would outliers affect the mean compared to the median?
  3. What other measures of central tendency exist besides mean, median, and mode?
  4. How can you calculate the range of this data set?
  5. What is the significance of the mode when the data has no repeating values?

Tip: The mean is sensitive to extreme values (outliers), while the median provides a better center for skewed distributions.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean = (sum of all values) / (number of values)
Median = middle value in a sorted list
Mode = value(s) that occur most frequently

Theorems

Mean Theorem
Median as a Measure of Central Tendency
Mode in Statistical Distributions

Suitable Grade Level

Grades 7-10