A useful tool to help us to understand our data is a histogram. Remember with check sheets we counted how many times different things occurred. That number is also called a frequency. The histogram is a graphic representation or a picture of what that frequency distribution looks like. Typically, it's a special type of bar graph. The vertical axis represents the frequency or how many times something happened. And the horizontal axis represents the various events or the things that happen. We can use our frequency table to construct a histogram. Again, this might be simple counts of things or events, this is also called the discrete data. Or if we have measurements, which may be continuous data, we will need to group those measurements and count how many times our measures fell in those groups. The intervals are shown on the X-Axis across the bottom. The number of scores or frequency is shown by the height of the rectangle located above the interval on the Y-Axis. In constructing a frequency table, and a histogram for measurement data, you need to determine how to group your measures. It's necessary to establish how many groups you need and how wide they will be. The number of groups is approximately equal to the square root of N, where N is the number of data points. For the width, just take the smallest value in your data set and subtract it from the largest. This is the range or the spread of your data. Divide that number by the number of groups that you determined in the first step. If the result is a fraction, just round up. All groups should be the same size if possible and there should be no overlap. Each value should fall into one and only one of the groups. For this example, let's look at some student grades on an exam. First, we might use a check sheet like we did before. The grades can be any number from 0 to 100, and any fraction in-between, so this is continuous data. We'll need to construct groups on our check sheet to reflect that. Then we'll create a tally by placing an x in the row next to each group for every student whose score falls into that group. When all of the grades have been tallied, we can add a totals column and count how many times each grade occurred. This is what the histogram of our grade data would look like. Notice we can also turn our check sheets sideways and get the same visual representation. What does this tell us? The first thing that we look for is whether or not the data is normally distributed. You've probably seen representations of the normal curve or the bell curve. Here we've placed a rough sketch of the normal curve over our histogram. We're not looking for an exact fit. Often, we may not have a lot of data. Small samples will not look exactly normal. For small amounts of data, like fewer than 50 data points, is the distribution higher near the middle and smaller as you move right to left? There are statistical tests for normality, but those will be covered in a future course. Is the data normally distributed? Where's the approximate center of the data? What's the spread of the data? That is, what are the differences between the lowest and highest values? Are there any outliers or unusual values? The answers to these questions can help you to determine what type of analysis you can do with the data. And you can get an idea of those values just by glancing at the histogram.