A total of 20 men and 20 women volunteer to participate in a statistics project. The height and weight of each subject are given in the table. Calculate the mean, variance, and standard deviation for height and weight in men and women.

Key Concepts

Mean

The mean is the average value of a set of numbers, calculated by summing all the values and dividing by the count of values. In the context of height and weight, it provides a central tendency that helps summarize the data for men and women. Understanding how to compute the mean is essential for analyzing the overall characteristics of the groups.

Variance

Variance measures the dispersion of a set of values around the mean, indicating how much the individual data points differ from the average. A higher variance signifies greater variability in height and weight among the subjects. This concept is crucial for understanding the spread of the data and is a foundational element in statistical analysis.

Standard Deviation

Standard deviation is the square root of the variance and provides a measure of the average distance of each data point from the mean. It is expressed in the same units as the original data, making it more interpretable. In this context, it helps to understand the variability in height and weight among the male and female participants.