This material is from section 2.1 in the textbook.

A simple list of numbers, even if short, is tough to decipher a pattern from. For this reason, statisticians and others working with data use summaries – either numerical or graphical – to help show the properties of a data set.

One popular, though somewhat technical graphical summary is the histogram. A histogram is really just a graph of a grouped frequency distribution, which is an idea we will study first.

Frequency distributions and grouped frequency distributions

A frequency distribution is just a way of representing counts. This may be the counts of how many times a value occurs or it may be a count of how many values fall into a range. In this second case, we sometimes say we have a grouped frequency distribution, though this distinction is not always necessary to make if it is clear in context. The focus of this lesson will be on grouped frequency distributions, which will be referred to as simply frequency distributions, for the sake of simplicity.

To understand a frequency distribution, we will learn how to make them! Now, typically we will want to use software for graphical displays of data, but if we have never made one by hand, we will not be very good at reading/adjusting the results. The video example below will go through this process. Keep in mind the following points:

the idea is to group the data in a way that makes it easy to see the big-picture pattern
groups (called "classes" or "bins" shouldn't be too small or two large)
when working by hand, we must first calculate the number of groups that we think might yield a good histogram and then go from there. This can be changed later if need be and commonly is when you are working with software.
Once you have a frequency distribution, you can sketch the corresponding histogram. This is included in the video!

Video example - making a frequency distribution and histogram by hand

The video uses this data set: Data for histogram example. You can also see a more detailed explanation of the math in this video here: http://www.mathbootcamps.com/making-frequency-distributions-and-histograms-by-hand/

Other information that can be included

There are some other common pieces of information that are added to a frequency distribution, depending on the application. These are the:

relative frequency, which is the % of the total frequency included in a class/group
cumulative frequency, which is a running total of the overall frequency

In the video below, you can see how to find these values.

Video example - relative and cumulative frequency

Shapes of histograms

As described in the textbook, histograms can often be described using some common shapes:

bell shaped/symmetric - a clear center with fewer and fewer data values as you get more extreme
left-skewed - a tail out to the left; most of the data is centered around larger values
right-skewed - a tail out to the right; most of the data is centered around smaller values

You can read more about shapes of histograms, including two others (bimodal and uniform) here: http://www.mathbootcamps.com/common-shapes-of-distributions/

Click NEXT to continue studying section 2.1.