Math Problem Statement

Make a box-and-whisker plot for 12, 13, 15, 16, 17, 18, 19, 21, 21, 23, 28, 28, 29, 31, 32, 35.

Solution

matplotlib.pyplot as plt

Data set

data = [12, 13, 15, 16, 17, 18, 19, 21, 21, 23, 28, 28, 29, 31, 32, 35]

Create the box-and-whisker plot

plt.figure(figsize=(8, 6)) plt.boxplot(data, vert=False, patch_artist=True, boxprops=dict(facecolor='lightblue')) plt.title("Box-and-Whisker Plot") plt.xlabel("Values") plt.grid(axis='x', linestyle='--', alpha=0.7) plt.show()Here is the box-and-whisker plot for the given data. It visually represents the distribution, showing the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

Would you like details about the quartiles or how the plot is constructed? Let me know! Here are five questions to expand your understanding:

  1. What are the steps to calculate quartiles from a data set?
  2. How does the presence of outliers affect the box-and-whisker plot?
  3. What is the significance of the interquartile range (IQR)?
  4. How would adding a new data point, like 40, impact this plot?
  5. Can a box-and-whisker plot be used to compare two different data sets?

Tip: A box-and-whisker plot is a great way to compare distributions and quickly identify data symmetry or skewness.

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Math Problem Analysis

Mathematical Concepts

Data Visualization
Descriptive Statistics
Box-and-Whisker Plot

Formulas

Quartiles: Q1, Median (Q2), Q3
Interquartile Range (IQR) = Q3 - Q1

Theorems

No specific theorems are directly applied, but statistical rules for quartile calculations are involved.

Suitable Grade Level

Grades 6-8