Math Problem Statement

What is the mean, median, minimum, maximum, Q1, Q3, and standard deviation of the data set?

What is the mean, median, minimum, maximum, Q1, Q3, and standard deviation of the data set?

Solution

Here are the statistical measures for the given data set of median incomes:

  • Mean: 63.94
  • Median: 61.9
  • Minimum: 46.5
  • Maximum: 87.1
  • Q1 (First Quartile): 56.78
  • Q3 (Third Quartile): 70.9
  • Standard Deviation: 10.13

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

  1. How is the standard deviation helpful in interpreting the data set?
  2. What does the difference between Q1 and Q3 (interquartile range) tell us about the distribution of data?
  3. How does the median compare to the mean in this data set?
  4. What effect do outliers have on the mean versus the median?
  5. How would changing the highest value affect the standard deviation?

Tip: The median is often a better measure than the mean when dealing with skewed data, as it is less affected by extreme values.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Measures of Central Tendency
Dispersion

Formulas

Mean: sum(data) / n
Median: middle value of sorted data
Standard Deviation: sqrt(sum((x - mean)^2) / n)

Theorems

Quartiles split data into four equal parts
Standard deviation measures the dispersion of data from the mean

Suitable Grade Level

Grades 9-12