What Is Descriptive Statistics? - Examples & Concept

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  • 0:02 What Are Descriptive…
  • 1:07 Measures of Central Tendency
  • 3:27 Measures of Dispersion
  • 5:51 Inferential Statistics
  • 6:34 Lesson Summary
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Lesson Transcript
Yolanda Williams

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

Expert Contributor
Jerry Allison

Jerry holds a Doctor of Business Administration and a Master’s in Mathematics. He has taught business, math, and accounting for over 25 years.

Descriptive statistics are used to summarize data. Learn about the different kinds of descriptive statistics, the ways in which they differ from inferential statistics, how they are calculated, and more.

What Are Descriptive Statistics?

Imagine that you are interested in measuring the level of anxiety of college students during finals week in one of your courses. You have 11 study participants rate their level of anxiety on a scale from 1 to 10, with 1 being 'no anxiety' and 10 being 'extremely anxious.' You collect the ratings and review them. The ratings are 8, 4, 9, 3, 5, 8, 6, 6, 7, 8, and 10. Your teacher asks you for a summary of your findings. How do you summarize this data? One way we could do this is by using descriptive statistics.

Descriptive statistics are used to describe or summarize data in ways that are meaningful and useful. For example, it would not be useful to know that all of the participants in our example wore blue shoes. However, it would be useful to know how spread out their anxiety ratings were. Descriptive statistics is at the heart of all quantitative analysis.

So how do we describe data? There are two ways: measures of central tendency and measures of variability, or dispersion.

Central tendency describes the central point in a data set. Variability describes the spread of the data.
central tendency

Measures of Central Tendency

You are probably somewhat familiar with the mean, but did you know that it is a measure of central tendency? Measures of central tendency use a single value to describe the center of a data set. The mean, median, and mode are all the three measures of central tendency.

The mean, or average, is calculated by finding the sum of the study data and dividing it by the total number of data. The mode is the number that appears most frequently in the set of data.

The median is the middle value in a set of data. It is calculated by first listing the data in numerical order then locating the value in the middle of the list. When working with an odd set of data, the median is the middle number. For example, the median in a set of 9 data is the number in the fifth place. When working with an even set of data, you find the average of the two middle numbers. For example, in a data set of 10, you would find the average of the numbers in the fifth and sixth places.

The mean and median can only be used with numerical data. The mode can be used with both numerical and nominal data, or data in the form of names or labels. Eye color, gender, and hair color are all examples of nominal data. The mean is the preferred measure of central tendency since it considers all of the numbers in a data set; however, the mean is extremely sensitive to outliers, or extreme values that are much higher or lower than the rest of the values in a data set. The median is preferred in cases where there are outliers, since the median only considers the middle values.

Knowing what we know, let's calculate the mean, median, and mode using the example from before. Again, the anxiety ratings of your classmates are 8, 4, 9, 3, 5, 8, 6, 6, 7, 8, and 10.

Mean: (8+ 4 + 9 + 3 + 5 + 8 + 6 + 6 + 7 + 8 + 10) / 11 = 74 / 11 = The mean is 6.73.

Median : In a data set of 11, the median is the number in the sixth place. 3, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10. The median is 7.

Mode: The number 8 appears more than any other number. The mode is 8.

Measures of Dispersion

We've got some pretty solid numbers on our data now, but let's say that you wanted to look at how spread out the study data are from a central value, i.e. the mean. In this case, you would look at measures of dispersion, which include the range, variance, and standard deviation.

The simplest measure of dispersion is the range. This tells us how spread out our data is. In order to calculate the range, you subtract the smallest number from the largest number. Just like the mean, the range is very sensitive to outliers.

The variance is a measure of the average distance that a set of data lies from its mean. The variance is not a stand-alone statistic. It is typically used in order to calculate other statistics, such as the standard deviation. The higher the variance, the more spread out your data are.

There are four steps to calculate the variance:

  1. Calculate the mean.
  2. Subtract the mean from each data value. This tells you how far each value lies from the mean.
  3. Square each of the values so that you now have all positive values, then find the sum of the squares.
  4. Divide the sum of the squares by the total number of data in the set.

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Additional Activities

Descriptive Statistics Thought Questions

Calculation Exercise

Suppose there are a group of 10 students taking a class at NoGo University. The students took a test and got the following grades: 65, 72, 78, 80, 81, 86, 89, 91, 92, 99. Calculate the descriptive statistic values of mean, median, and mode for this data.

Research Exercise

The lesson mentioned the measures of central tendency to be the mean, median, and mode. Search on the Internet to find other measures of central tendency. The lesson mentioned the measures of dispersion to be the range, variance, and standard deviation. Search again on the Internet to find other measures of dispersion. Which measures of central tendency are the most commonly used? Which measures of dispersion are most commonly used? Why are the other measurements of central tendency and of dispersion not commonly used? Write a report explaining your findings.

Calculation Exercise

The Mega Calorie Diet has been designed to help people gain weight. A group of five people on this diet gain 10 pounds, 15 pounds, 14 pounds, 8 pounds, and 13 pounds. The inventors of the diet want to know the measures of dispersion for this data, namely, range, variance, and standard deviation. Please calculate these values for them.

Discussion Exercise

Descriptive statistics are used frequently in quality assurance to describe a sample from a manufacturing process. Both the measures of central tendency and dispersion are monitored. Discuss what is happening with the items produced if the measures of central tendency are too high or too low. Then discuss what is happening with the items produced if the measures of dispersion are high or low. Is it possible for the measures of central tendency to be extreme, but the measures of dispersion to be fine? Is it possible for the measures of dispersion to be extreme, but the measures of central tendency to be fine?

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