## Descriptive Analysis Tools

#### To help you develop your own descriptive analysis summaries for your research, we have identified commonly used descriptive analysis methods with accompanying tools and resources. In this page, concepts will be explained and examples are provided from published studies to demonstrate how you can implement these methods into your research.

## Foundation—Measures of Central Tendency

#### So you reviewed the foundational video and understand the mean, median, and mode concepts. What next? In addition to understanding these terms, it’s important that you also know how to apply this to your research. For example, understanding the difference between populations, samples, parameters and statistics, as well as how to utilize measures of central tendency to describe different aspects of your research. Watch and practice:

#### 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.

#### Comparing means of distribution:

#### Mean and Medians of Different Distributions:

#### 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 the sample mean, we can infer things about the greater population mean. We explain:

#### Click here to access the measure of central tendency calculator.

## Box and Whisker Plots

#### Are a graphic way to display the median, quartiles, and extremes of a data set on a number line to show the distribution of the data.Box whisker plots seek to explain data by showing the spread of all the data points in a sample, the “whiskers” are the two opposite ends of the data. Watch:

#### Here is a world problem perfectly suited for a box and whisker plot to help analyze data. We can construct this together here or you can scroll down and use the box and whisker plot tool to build your own graph with your data.

#### The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number. You can practice here:

#### Click here to build your own box plot

#### Click here to learn how to build a box plot in excel

## Variance and Standard Deviation

#### We have tools (like the arithmetic mean) to measure central tendency and are now curious about representing how much the data in a set varies from that central tendency. In this tutorial we introduce the variance and standard deviation (which is just the square root of the variance) as two commonly used tools for doing this.

#### Variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean and subsequently to each other, while a high variance indicates that the data points are very spread out around the mean and from each other.

#### Range is the difference between the lowest and highest values. In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the **range** is 9 − 3 = 6. Range can also mean all the output values of a function.

#### Watch how the range, variance, and standard deviation can be measures of dispersion:

#### Watch the variance of a population, meaning on average how far the data points in a population are from the population mean.

#### Sample variance, the ability to think about how we can estimate the variance of a population by looking at a data in a sample.

#### Sample variance allows us to think about how we can estimate the variance of a population by looking at the data in a sample.

#### This simulation by Peter Collingridge gives us a better understanding of why we divide by (n-1) when calculating the unbiased sample variance. The simulation is also available here.

**Population standard deviation**: