Section 3.3 Summary

1. The weighted mean is the sum of the products of the data points with their respective weights, divided by the sum of the weights.
2. We do not have access to the original raw data, so it is not possible to find exact values for the mean, variance, and standard deviation of data that have been grouped into a frequency distribution. The estimated mean, , in this case is the sum of the products of the class frequencies, , and class midpoints, , divided by the sum of the frequencies, .
3. Class midpoints and class frequencies are also used to find the estimated variance, , and estimated standard deviations of grouped data.