Math Problem Statement

Consider the following dataset: 244, 361, 294, 100, 439, 285, 291, 307, 186, 24, 180, 363, 475, 285. Calculate the standard deviation. Write the 5-number summary for this data set. Calculate the Interquartile range. Identify any outliers. Show your working out. Construct a box plot showing the outliers.

Solution

The box plot above visualizes the dataset along with the 5-number summary, highlighting the minimum, Q1, median, Q3, and maximum values. As seen in the plot, there are no outliers.

Would you like further details on any of the steps, or do you have any other questions?

Here are 5 related questions that can deepen your understanding:

  1. How does changing the dataset affect the standard deviation?
  2. What is the relationship between IQR and the detection of outliers?
  3. How can you interpret skewness from the box plot?
  4. How would the 5-number summary change if outliers were present?
  5. What are the pros and cons of using a box plot compared to a histogram?

Tip: The interquartile range (IQR) is useful for comparing variability between datasets without being affected by extreme values.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Data Analysis

Formulas

Standard Deviation Formula
Five-Number Summary
Interquartile Range Formula

Theorems

Outlier Detection Rule (1.5 * IQR)

Suitable Grade Level

Grades 10-12