Math Problem Statement

Cholesterol levels collected from patients two days after they had a heart attack are in the table.

Cholesterol levels

157 308 205 306 301 279 253 306 280 223 206 302 217 169 223 257 150 290 302 301 176 318 288 149 195 280 257 214

Find the five-number summary and interquartile range (IQR), and draw a boxplot. Min = . Q1 = . Q2 = . Q3 = . Max = . IQR = .

Solution

Here is the boxplot representing the cholesterol levels two days after a heart attack. The red line inside the box indicates the median (Q2 = 257), and the box itself spans from Q1 (205.5) to Q3 (301). The whiskers extend to the minimum (149) and maximum (318) values.

Would you like more details or have any other questions?

Here are five related questions for further exploration:

  1. How are outliers identified in a boxplot?
  2. What is the importance of the interquartile range (IQR) in statistics?
  3. How would changing one data point affect the five-number summary?
  4. Can you calculate the standard deviation for this data set?
  5. What is the significance of cholesterol levels in heart attack recovery?

Tip: In a boxplot, values outside the whiskers are considered potential outliers, which might indicate unusual or extreme observations.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Five-Number Summary
Interquartile Range (IQR)

Formulas

Five-number summary: Min, Q1, Median (Q2), Q3, Max
Interquartile range (IQR) = Q3 - Q1

Theorems

Five-Number Summary Theorem: A method for summarizing a dataset using the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
IQR Theorem: A measure of statistical dispersion, or how spread out the middle 50% of values are.

Suitable Grade Level

Grades 10-12