Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.


Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that males have become heavier?

Verified step by step guidance

1. Step 1: Identify the relevant data sets. Locate the weights of males from Data Set 2 ('ANSUR I 1988') and Data Set 3 ('ANSUR II 2012') in Appendix B. Ensure you have access to the complete data for both years.
2. Step 2: Calculate the mean for each data set. Use the formula for the mean: $\mu =\frac{\sum x}{n}$, where $x$ represents individual weights and $n$ is the total number of weights in the data set. Use software or a calculator to sum the weights and divide by the total count.
3. Step 3: Calculate the median for each data set. Arrange the weights in ascending order. If the number of weights is odd, the median is the middle value. If the number of weights is even, the median is the average of the two middle values. Use software or a calculator to assist with sorting and finding the median.
4. Step 4: Compare the means and medians of the two data sets. Analyze whether the mean and median weights from 2012 (Data Set 3) are higher than those from 1988 (Data Set 2). This comparison will help determine if males appear to have become heavier over time.
5. Step 5: Interpret the results. Consider the context of the data, such as sample size and potential biases, to draw a conclusion about whether males have become heavier based on the calculated means and medians.

Key Concepts

Mean

The mean, or average, is a measure of central tendency calculated by summing all values in a data set and dividing by the number of values. It provides a single value that represents the overall level of the data, making it useful for comparing different data sets. However, the mean can be influenced by extreme values, which may skew the results.

Median

The median is another measure of central tendency that represents the middle value of a data set when it is ordered from least to greatest. If the data set has an even number of observations, the median is the average of the two middle values. The median is less affected by outliers and provides a better representation of the typical value in skewed distributions.

Comparative Analysis

Comparative analysis involves evaluating two or more data sets to identify differences or trends. In this context, it requires comparing the means and medians of male weights from two different years to assess whether there has been a significant change over time. This analysis helps in understanding patterns and making informed conclusions about the data.