Statistics: Basic Concepts

Frequency Polygons

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A **frequency polygon** shows the overall distribution of a data set. It looks a little bit like a line graph–but the points on the graph can be plotted using data from a **histogram** or a **frequency table**.

Frequency polygons are especially useful for **comparing two data sets**. In our example, we’ll use the histogram from the last lesson in order to make our frequency polygon.

How to create a frequency polygon

Here is our histogram from the previous lesson, which shows the age range of members of the orchestra:

**Step 1:**Imagine that at the top of each bar, there is a dot located right in the middle. These dots are called**midpoints**. (They are also sometimes referred to as “class marks.” This is because categories/bins are sometimes called classes).

Each midpoint marked on the graph represents the frequency of each bin or age range.

**Step 2:**Once the midpoints have been plotted, the first line segment should connect zero to the first midpoint.

**Step 3:**After that, we’ll connect the first midpoint to the second one, and so on.

**Step 4:**Remove the bars and copy your**value increments**onto the**x-axis**. Since we don't have the bars to represent each bin, make sure you're clear about what values are being shown on the x-axis. In this case, each point represents an**age range**.

**Step 5:**Now you have your frequency polygon!

Usually a frequency polygon is compared to a different frequency polygon on the same graph. The second frequency polygon comes from **another data set**.

For example, if you wanted to **compare** the age range of the band’s members from 10 years ago with the current band, you could do two things:

- Use
**frequency tables**for your two data sets to plot the points of your frequency polygons. - Make
**histograms**for each set of data, and then create frequency polygons from your histograms.

You would plot your frequency polygons on the same graph. Let’s use a **gray line** to represent the data set from 10 years ago, which we can compare with the **white line** representing the current band’s ages:

On the whole, the trends in the data appear quite similar. The conductor can see that there’s been a dip (or decline) in the 35-40 year age range.

Here’s a quick recap…

- Frequency polygons can be made from a histogram or a frequency table. If you are creating one using a histogram, plot the midpoints at the top of each bar. Then
**connect the midpoints**and remove each bar. - Generally frequency polygons are used to reflect
**quantitative data**. If you have “bins” like age ranges, these can be plotted on the x-axis. The y-axis is often used to reflect frequency. - They’re useful for comparing/contrasting two (or more)
**data sets reflected on the same graph**. Take a look at the overall distribution, and see what conclusions you can draw about the data.

In the next section of the tutorial, we’ll start diving into some **other fundamentals** that will help you in statistics.

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