Math Problem Statement

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

Cholesterol levels 313 222 210 300 181 269 144 144 198 187 244 241 279 217 157 313 171 195 187 155 146 220 200 168 304 220 309 173

Find the mean, median, range, variance, and standard deviation using technology. Round to the nearest tenth, if necessary.

Solution

For the given cholesterol levels, the statistical measures are:

  • Mean: 216.7
  • Median: 205.0
  • Range: 169
  • Variance: 3078.6
  • Standard Deviation: 55.5

Would you like more details or have any questions?

Here are 5 related questions you can explore:

  1. How does the mean change if an additional cholesterol value is added?
  2. What is the difference between sample variance and population variance?
  3. How is the range influenced by extreme values in the dataset?
  4. What is the importance of the standard deviation in medical statistics?
  5. Can you explain how skewness might affect the median and mean?

Tip: The standard deviation is a critical measure for understanding the variability of data around the mean—especially useful in medical data analysis to assess consistency.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Spread

Formulas

Mean = (Sum of all data points) / (Number of data points)
Median = Middle value of the ordered data set
Range = Maximum value - Minimum value
Variance (Sample) = Σ(xi - mean)^2 / (n - 1)
Standard Deviation = √Variance

Theorems

Central Limit Theorem (related in terms of statistical analysis)
Properties of Mean and Variance

Suitable Grade Level

Grades 10-12

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