2015

Introduction to Normal Distribution in Statistics

A continuous random variable has an infinite number of values that can be represented by an interval on the number line. It’s probability distribution is called a continuous probability distribution. In this article, we will be understanding the most important continuous probability distribution in statistics, the normal distribution.

A normal distribution is a continuous probability distribution for a random variable, x. The graph of a normal distribution is called the normal curve. A normal distribution has the following properties.

1. The mean, median and mode are equal.

2. The normal curve is bell-shaped and is symmetric about the mean.

3. The total area under the normal curve is equal to 1.

4. The normal curve approaches, but never touches the x-axis as it extends farther and farther away from the mean.

5. Between m - s and m + s (in the center of the curve) the graph curves downward. The graph curves upward to the left of m - s and to the right of m + s. The points at which the curve changes from curving upward to curving downward are called inflection points.

6. A normal distribution can have any mean and any positive standard deviation. These two parameters, m and s completely determine the shape of a normal curve. The mean gives the location of the line of symmetry and the standard deviation describes how much the data are spread out.

See the line of symmetry for each? That’s the mean. However, if it is fatter, then the standard deviation is greater. That’s the difference.

Understanding Mean & Standard Deviation

Which normal curve has a greater mean?

Which normal curve has a greater standard deviation

The line of symmetry of curve A occurs at x = 15. The line of symmetry of curve B occurs at x = 12. So, curve A has a greater mean.

Curve B is more spread out than curve A, so curve B has a greater standard deviation.

The Empirical Rule

In a normal distribution with mean m and standard deviation s, you can approximate areas under the normal curve as follows:

1. About 68% of the area lies between m - s and m + s
2. About 95% of the area lies between m - 2s and m + 2s
3. About 99.7% of the area lies between m - 3s and m + 3s

Storytelling with Data - Web Analysis

Why Storytelling?
Visual analysis means exploring data visually. A story unfolds as you navigate from one visual summary into another.
You and your team have sorted through and analyzed a dense data set, made industry-relevant discoveries and created data visualizations that allow you to share those insights with others—whether other team members, current or potential clients, or the community at large. Before you present your work, think about your audience and the goals you want to achieve.
Keep in mind that the people you want to communicate with may not have the same background or technical knowledge that you do. Although eager to understand, audience members may need additional explanation, simplified insights or a more slowly paced presentation to grasp your point of view. Making the data accessible to your audience is your responsibility.
A tried-and-true method of connecting with your audience is to embed your data insights within a story. The story framework will capture your audience's attention and help you meet the business objectives driving your work.

Story Framework
Before you embark on your data journey, identify the questions you want to answer. You may have a specific question in mind or a general area you'd like to explore. As you dig into your data, you may find an entirely new or unexpected story, but it helps to have a starting point.

An example of one story framework for a web analysis example on how to visualize online campaign performance.

and the output...