How to find average and variance

The calculation of the average is one of the most common methods of generalization. The average reflects all things in common, which is typical for the characteristics of the aggregate. But at the same time, he ignores the differences of the individual units.

Instruction

1. The most common in the calculation is a simple average. You can easily find if there is a set of two or more statistical indicators, arranged in any order. Simple arithmetic average is defined as the ratio of the sum of the individual values of the attribute to the number of features in combination: Khsr = ?XI/n.
2. If the volume of the aggregate is large and represents the number distribution, the calculation must use the weighted arithmetic mean. This way you can determine, for example, the average price per unit: total value of products (product of the number of each type in the price) are divided by the total volume of products: Khsr = ?XI*fi/?fi. In other words a weighted average is defined as the ratio of sums of products of characteristic values and the frequency of repetition of the sign of the sum of the frequencies of all features. It is used in cases where the options researched population occur different number of times.
3. In some cases you need to apply in the calculation of the average harmonic. It is used when you know the individual characteristic values x and fx work, and the value of f is not known: Khsr = ?wi/?(wi/XI), where wi = XI*fi. If the individual characteristic values meet once (all wi =1), the harmonic average is applied is simple: Khsr = N/?(wi/XI).
4. The variance you can calculate as follows: D = ?(X-Khsr)^2/N, in other words the variance is the average squared deviation from the mean value. There is another way of calculating this indicator: D = (X^2)CP – (Khsr)^2. The variance difficult to interpret meaningful. However, the square root of it characterizes standard deviation. It reflects the average deviation of the characteristic from the average value of the sample.