Math Problem Statement

Question content Part 1 Listed below are pulse rates​ (beats per​ minute) from samples of adult males and females. Find the mean and median for each of the two samples and then compare the two sets of results. Does there appear to be a​ difference?

​Male: 76 88 54 80 63 82 58 70 61 84 56 57 57 74 77 ​Female: 73 75 92 95 84 68 93 69 87 92 88 87 83 89 79 Question content area bottom Part 1

The mean for males is 69.1 beats per minute and the mean for females is 83.6 beats per minute. ​ Part 2 Find the medians. The median for males is 70 beats per minute and the median for females is 87 beats per minute. ​ Part 3 Now, I need you to compare the results. Choose the correct answer below. A. The mean and the median for females are both lower than the mean and the median for males. B. The mean and the median for males are both lower than the mean and the median for females. C. The mean is lower for​ males, but the median is lower for females.D. The median is lower for​ males, but the mean is lower for females. E. The mean and median appear to be roughly the same for both genders.

Solution

Let's analyze the given data to compare the results.

Given Data:

  • Males' Pulse Rates: 76, 88, 54, 80, 63, 82, 58, 70, 61, 84, 56, 57, 57, 74, 77
  • Females' Pulse Rates: 73, 75, 92, 95, 84, 68, 93, 69, 87, 92, 88, 87, 83, 89, 79

Summary of Given Results:

  • Mean Pulse Rate for Males: 69.1 beats per minute
  • Mean Pulse Rate for Females: 83.6 beats per minute
  • Median Pulse Rate for Males: 70 beats per minute
  • Median Pulse Rate for Females: 87 beats per minute

Comparison:

  • The mean for males (69.1) is lower than the mean for females (83.6).
  • The median for males (70) is also lower than the median for females (87).

Correct Answer:

B. The mean and the median for males are both lower than the mean and the median for females.

Would you like any further details or explanations?

Here are 5 related questions:

  1. How would the comparison change if the sample sizes were different for males and females?
  2. What does the median tell us about the distribution of pulse rates for each gender?
  3. How can the standard deviation further describe the pulse rate differences between genders?
  4. What effect might outliers have on the mean and median in this dataset?
  5. How could this analysis be used to compare pulse rates across different age groups?

Tip: When comparing two datasets, always consider both the mean and median to understand the central tendency and distribution, as they can provide complementary information.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Mean
Median

Formulas

Mean = (Sum of values) / (Number of values)
Median = Middle value when data is ordered

Theorems

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Suitable Grade Level

Grades 6-8