Normal Distribution of Data: Examples, Definition & Characteristics

Normal Distribution of Data: Examples, Definition & Characteristics
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  • 0:01 Data and Distribution
  • 0:33 What Is Normal Distribution?
  • 1:02 Characteristics of…
  • 1:52 Percentiles
  • 2:55 Example
  • 4:11 Lesson Summary
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Lesson Transcript
Instructor: Yolanda Williams

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

In this lesson, we'll explore the normal distribution of data. Learn about the characteristics of normal distribution, how to plot histograms, the empirical rule, and more.

Data and Distribution

Imagine that you are a professor teaching an intro to psychology course. At the end of the semester, you have all 100 of your students complete a final exam consisting of 100 multiple-choice questions. The scores that your students received are as follows:

You can tell from looking at the data that the highest score a student received was 100% and the lowest score was 60%. What you might not have been able to tell just by glancing at the table is that the data is normally distributed.

What Is Normal Distribution?

A normal distribution is a bell-shaped frequency distribution curve. Most of the data values in a normal distribution tend to cluster around the mean. The further a data point is from the mean, the less likely it is to occur. There are many things, such as intelligence, height, and blood pressure, that naturally follow a normal distribution. For example, if you took the height of one hundred 22-year-old women and created a histogram by plotting height on the x-axis, and the frequency at which each of the heights occurred on the y-axis, you would get a normal distribution.

Characteristics of Normal Distribution

Here, we see the four characteristics of a normal distribution. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal.

A normal distribution is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side. There is also only one mode, or peak, in a normal distribution. Normal distributions are continuous and have tails that are asymptotic, which means that they approach but never touch the x-axis. The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below. It follows that the mean, median, and mode are all equal in a normal distribution.


Now, look at the line that says standard deviations (SD). You can see that 34.13% of the data lies between 0 SD and 1 SD. Since a normal distribution is perfectly symmetric, it follows that 34.13% of the data lies between -1 SD and 0 SD. If you continue to add the percentages together, you will see that on either side:

  • Approximately 68% of the data lies within 1 SD of the mean
  • Approximately 95% of the data lies within 2 SD of the mean
  • Approximately 99.7% of the data lies within 3 SD of the mean

This is known as the empirical rule.

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