4.1:
What is Variation?
Recall that the measures of center, variation, distribution, outliers, and changing data characteristics over time are essential for effective data analysis. Of these, the measures of variation describe the dispersion or spread of the values in a dataset.
Consider the datasets on heights of randomly selected school children and that of students of a particular grade. Although the plots of the two datasets have the same mean, they vary significantly in how data points are dispersed or positioned. The plot on the left has the values more spread out than the one on the right.
Therefore, instead of the mean, variation is used to measure the spread of values in the datasets. Range, standard deviation, and variance are commonly used measures of variation.
The range is the difference between the maximum and minimum data values.
The standard deviation measures how much the data value varies about the mean, while the variance is the square of the standard deviation.
Thus, each measure of variation helps to uniquely analyze and interpret the differences between datasets.
4.1:
What is Variation?
Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
The range, standard deviation, standard error, and variance are the different measures of variation.
Range: The range is the difference between its maximum and minimum values.
Standard Deviation: It is the most commonly used measure of variation. A standard deviation is a number that measures how far data values are from their mean. The standard deviation provides a numerical measure of the overall amount of variation in a data set,
Standard error: The standard error of the mean is a special kind of standard deviation, which measures the variation of a statistic from one sample to another.
Variance: The variance is a measure of variation which is numerically given as the square of the standard deviation.
Thus, each measure of variation gives a unique insight into the interpretation and comparison of data values or samples.
This text is adapted from 2.7 Measures of the Spread of the Data – Introductory Statistics | OpenStax