#Define activity variance formula how to#

The equations given above show you how to calculate variance for an entire population. These measures are useful for making comparisons between data sets that go beyond simple visual impressions. The variance and the standard deviation give us a numerical measure of the scatter of a data set. The difference between the plant with the highest number of leaves and the lowest number of leaves is 10, so the data has relatively high variance. All plants have different number of leaves ranging from 1 to 11. We'll start by assigning each number to variable, X 1– X 6, like this:Ī histogram showing the number of plants that have a certain number of leaves. The summation operator is just a shorthand way to write, 'Take the sum of a set of numbers.' As an example, we'll show how we would use the summation operator to write the equation for calculating the mean value of data set 1. In order to write the equation that defines the variance, it is simplest to use the summation operator, Σ. The standard deviation ( σ) is simply the (positive) square root of the variance. Divide the sum of the squares by the number of values in the data set.

Square each of these distances (so that they are all positive values), and add all of the squares together.This gives you a measure of the distance of each value from the mean. Subtract the mean from each value in the data.The variance ( σ 2) is a measure of how far each value in the data set is from the mean. The measure should be independent of the mean (since now weĪre only interested in the spread of the data, not its centralīoth the variance and the standard deviation meet these three criteria for normally-distributed (symmetric, 'bell-curve') data sets.Value would increase even if the scatter of the measurements was not In the data set (otherwise, simply by taking more measurements the The measure should be independent of the number of values.The data (small when the data are clustered together, and large when The measure should be proportional to the scatter of.It would be useful to have a measure of scatter that has the following properties:

Define activity variance formula