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.

Verified step by step guidance

1. Organize the data by separating the height and weight values for men and women into four distinct groups: men's heights, men's weights, women's heights, and women's weights.
2. Calculate the mean (average) for each group using the formula: $\mathrm{mean}=\frac{\sum x}{n}$, where $x$ represents each individual measurement and $n$ is the number of individuals (20 in this case).
3. Compute the variance for each group by first finding the squared difference between each measurement and the mean, then averaging these squared differences using the formula: $\mathrm{variance}=\frac{\sum {x-\mathrm{mean}}^2}{n}$.
4. Determine the standard deviation for each group by taking the square root of the variance, expressed as: $\mathrm{standard\; deviation}=\; \surd \mathrm{variance}$.
5. Summarize the results by listing the mean, variance, and standard deviation for height and weight separately for men and women, ensuring clarity in the presentation of each statistical measure.

Key Concepts

Mean

The mean is the average value of a data set, calculated by summing all observations and dividing by the number of observations. It provides a measure of central tendency, representing the typical value in the data, such as average height or weight.

Variance

Variance measures the spread or dispersion of data points around the mean. It is calculated as the average of the squared differences between each data point and the mean, indicating how much the values vary within the group.

Standard Deviation

Standard deviation is the square root of the variance and expresses data variability in the same units as the original measurements. It quantifies the typical distance of data points from the mean, helping to understand the consistency of height or weight within men or women.