Descriptive statistics

Statistics intro: Mean, median and mode

This is a fantastic intro to the basics of statistics. Our focus here is to help you understand the core concepts of arithmetic mean, median, and mode.

Finding mean, median and mode

Here we give you a set of numbers and then ask you to find the mean, median, and mode. It's your first opportunity to practice with us!

Exploring the mean and median

Watch as we use a nifty interactive module to demonstrate how moving points along a number line can help us find the mean and median.

Inferring population mean from sample mean

Much of statistics is based upon using data from a random sample that is representative of the population at large. From that sample mean, we can infer things about the greater population mean. We'll explain.

Box and whisker plot

Is this some kind of cute cat video? No! Box and whisker plots seek to explain data by showing a spread of all the data points in a sample. The "whiskers" are the two opposite ends of the data. This video is more fun that a handful of catnip.

Constructing a box and whisker plot

Here's a word problem that's perfectly suited for a box and whiskers plot to help analyze data. Let's construct one together, shall we?

Constructing a box and whisker plot

Here's a word problem that's perfectly suited for a box and whiskers plot to help analyze data. Let's construct one together, shall we?

Finding the range and mid-range

The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number. Practice with this problem.

Variance of a population

Variance as a measure of, on average, how far the data points in a population are from the population mean

Sample variance

Thinking about how we can estimate the variance of a population by looking at the data in a sample.

Review and intuition why we divide by n-1 for the unbiased sample variance

Reviewing the population mean, sample mean, population variance, sample variance and building an intuition for why we divide by n-1 for the unbiased sample variance

Simulation showing bias in sample variance

Simulation by Peter Collingridge giving us a better understanding of why we divide by (n-1) when calculating the unbiased sample variance. Simulation available at: http://www.khanacademy.org/cs/challenge-unbiased-estimate-of-population-variance/1169428428

Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance

Another visualization providing evidence that dividing by n-1 truly gives an unbiased estimate of population variance. Simulation at: http://www.khanacademy.org/cs/unbiased-variance-visualization/1167453164

Simulation providing evidence that (n-1) gives us unbiased estimate

Simulation by KA user tetef showing that dividing by (n-1) gives us an unbiased estimate of population variance. Simulation at: http://www.khanacademy.org/cs/will-it-converge-towards-1/1167579097

Statistics: Standard deviation

Review of what we've learned. Introduction to the standard deviation.

Exploring standard deviation 1 module

Ben Eater and Sal Khan talk through the Khan Academy Standard Deviation 1 Module: http://www.khanacademy.org/math/statistics/e/exploring_standard_deviation_1

Statistics: Alternate variance formulas

Playing with the formula for variance of a population.

Statistics: The average

Introduction to descriptive statistics and central tendency. Ways to measure the average of a set: median, mean, mode

Statistics: Variance of a population

Variance of a population.

Statistics: Sample variance

Using the variance of a sample to estimate the variance of a population