Chapter 3: Problem 23

Find the mean and median for each of the two samples, then compare the two sets of results. Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 "Body Data" in Appendix B). Does there appear to be a difference? $$\begin{array}{llllllllllll}\text { Male: } & 86 & 72 & 64 & 72 & 72 & 54 & 66 & 56 & 80 & 72 & 64 & 64 & 96 & 58 & 66 \\\\\text { Female: } & 64 & 84 & 82 & 70 & 74 & 86 & 90 & 88 & 90 & 90 & 94 & 68 & 90 & 82 & 80\end{array}$$

### Short Answer

## Step by step solution

## - List the data

## Male Data

## Female Data

## - Calculate Mean of Male Pulse Rates

## - Calculate Median of Male Pulse Rates

## - Calculate Mean of Female Pulse Rates

## - Calculate Median of Female Pulse Rates

## - Compare the Results

## Key Concepts

These are the key concepts you need to understand to accurately answer the question.

###### Mean Calculation

For example, with the male pulse rates given in the exercise, we sum all the values (86, 72, 64, etc.) to obtain a total of 1132. Next, we divide this total by the number of data points, which is 15. The resulting mean for the male pulse rates is calculated as: \(Mean_{male} = \frac{1132}{15} = 75.47\)

Similarly, for the female pulse rates, summing all values gives us 1222. We again divide by the number of data points, which is 15. The mean for the female pulse rates is: \(Mean_{female} = \frac{1222}{15} = 81.47\). Summarizing, the mean helps to understand the general tendency or average value around which all data points lie.

###### Median Calculation

- Sort the dataset in ascending order.
- If the number of data points is odd, the median is the middle number.
- If the number of data points is even, the median is the average of the two middle numbers.

After ordering the data: 54, 56, 58, 64, 64, 64, 66, 66, 72, 72, 72, 80, 86, 96.

With 15 values, the 8th value (66) is the median: \(Median_{male} = 66\)

For female pulse rates:

Ordered: 64, 68, 70, 74, 80, 82, 82, 84, 86, 88, 90, 90, 90, 90, 94.

The middle value, the 8th one (84), is the median: \(Median_{female} = 84\). Using the median helps identify the central value, especially useful if the dataset contains outliers.

###### Comparing Distributions

In the exercise, we have two distributions: male and female pulse rates. Let's compare them:

**Mean:**Mean pulse rates for males (75.47) is less than that for females (81.47).**Median:**Median pulse rate for males (66) is significantly less than that for females (84).

###### Data Analysis

From the given details, data points were initially listed for two groups: male and female.

- Summing the values
- Calculating averages
- Ordering data for median

The results showed:

- Females have higher mean (81.47 vs. 75.47).
- Females also have a higher median pulse rate (84 vs. 66).