Measures of Dispersion/Variability | Range, Variance, Standard Deviation | Statistics for Beginners

Introduction

In this video, the speaker talks about measures of dispersion or variability and why they are important in describing a set of data.

Measures of Dispersion or Variability

• Dispersion refers to how similar or different data points are in a set.

• Three common measures of dispersion are range, variance, and standard deviation.

• Measures of central tendency (such as mean) do not provide information on the spread of data points.

• Two sets of data can have the same mean but different levels of variability.

Range

• The range is the difference between the highest and lowest values in a dataset.

• The range is not commonly used because it only provides a rough estimate of variability.

Variance

• Variance is a more commonly used measure of dispersion that provides a more accurate estimate than range.

• Population variance is used when computing from an entire population.

Measures of Dispersion

In this section, the speaker discusses the three measures of dispersion or variability: range, variance, and standard deviation. The speaker explains how to compute each measure and provides examples.

Population Variance vs Sample Variance

• The formula for computing population variance is almost the same as that for computing sample variance.

• The major difference between the two is the denominator. For population variance, it's "n" (number of observations), while for sample variance, it's "n-1".

• When computing summation notations, "summation of x" means summing all data points in a population. "Summation of x squared" means squaring each data point before taking the sum.

Example Computation

• To illustrate how to compute sample variance, an example is given using scores from 12 students.

• First, compute the sum of all data points in the sample.

• Answer: 470

• Next, compute the sum of squared observations.

• Answer: 19668

• Substitute these values into the formula for sample variance.

• Denominator: 12 - 1 = 11

• Answer: 114.52 (approx.)

Standard Deviation

• Standard deviation is another measure of dispersion/variability.

• It's related to variance by taking its square root.

• To compute standard deviation from a given set of data points:

• Compute its variance first using either population or sample formula.

• Take its square root to get standard deviation.

Example Computation Continued

• Using the previous example computation where we got a sample variance value of 114.52:

• Answer: 10.70