Math Problem Statement

Cholesterol levels (mg/dL) were collected from a random sample of 21 patients two days after they had a heart attack.

Cholesterol level 226 294 288 280 220 282 242 272 160 282 236 276 224 266 280 210 206 244 142 278 186

For the data shown above, find the following. Round values 1 decimal place(s). Select the correct units for each statistic.

Find the mean:

Select an answer Find the median:

Select an answer Find the range:

Select an answer Find the variance:

Select an answer Find the standard deviation:

Select an answer

Solution

Here are the calculated statistics for the cholesterol levels:

  1. Mean: 242.6 mg/dL
  2. Median: 244.0 mg/dL
  3. Range: 152 mg/dL
  4. Variance: 1905.7 (mg/dL)2(\text{mg/dL})^2
  5. Standard Deviation: 43.7 mg/dL

Would you like more details on any of these calculations?

Here are five related questions to explore further:

  1. What does the standard deviation indicate about cholesterol level variation in this sample?
  2. How would the mean and median change if we removed an outlier?
  3. How does the range relate to the spread of cholesterol levels in this group?
  4. Why is it essential to consider the variance and standard deviation in medical studies?
  5. What are potential factors that might influence the variance in cholesterol levels after a heart attack?

Tip: For small samples, the sample standard deviation (using n−1n-1 in the formula) provides a better estimate of population variability.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion

Formulas

Mean: \( \text{Mean} = \frac{\sum x}{n} \)
Median: Sort data and find the middle value (or average of two middle values if n is even)
Range: \( \text{Range} = \text{Max value} - \text{Min value} \)
Variance: \( s^2 = \frac{\sum (x - \bar{x})^2}{n - 1} \)
Standard Deviation: \( s = \sqrt{\text{Variance}} \)

Theorems

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Suitable Grade Level

Grades 10-12

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