15 - WEIGHTED AVERAGES, DEATH RATES AND TIME SERIES

Abstract

This chapter discusses weighted averages, death rates, and time series. The weights w1 w2, w3, … wn are used to give more (large value of w) or less (small value of w) importance to the effect of x1, x2, … xn in calculating the final weighted average. In many applications of statistics, especially in economics, one wishes to compare different sets of data. To do this, the data is reduced to purely relative numbers by comparing it with a fixed base value. Such relative numbers are the simplest index numbers, they are known as price relatives, and are generally expressed as percentages. Another way of calculating a simple index number is to compare the total price of buying equal quantities of different types of goods with the total price some time later, or in a different region. To obtain a standardized death rate, a standard population is used as a basis for comparison. As the mortality rates for males and females differ considerably, the distribution of the population is given in two parts. To calculate the standardized death rate, the crude death rates are found for each group under consideration. A time series is a set of observations taken at different times, usually at equal intervals.