Creating Frequency Distributions

Using the formula above, we have that \[\begin{align*}\text{class width } = \dfrac{\text{largest value } - \text{smallest value }}{\text{number of classes}}=\dfrac{75-0}{{6}}\approx 12.5\end{align*}\]

Since our output gave use a decimal, we round it up to the next integer.  Therefore, our class width will be 13.

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We just start at 7 and keep adding 10 and until we get a number larger than 75.  So, the boundary points starting with 5 are \[7,\qquad 17,\qquad 27,\qquad 37,\qquad 47,\qquad 57,\qquad 67,\qquad 77\]

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The data from should already be loaded into GeoGebra.  If it is not, follow the steps at the beginning of to load the data in and selected option B from the dropbox.  Your tool should like this:

The first thing we are going to do is check the Organize Data into Classes checkbox.  Multiple new options appear: Lower Class Boundary, Class Width, Number of Classes. (There are other new options; we can ignore them for now.)  Notice that the Lower Class Boundary will automatically become the value of the smallest data point; the class width and number of classes will default to preassigned values.

First, we want to calculate the class width.  Since we want 8 classes, we will enter that value info class width.  Notice that the number of classes will update to 10 since \[\begin{align*}\text{class width }&= \dfrac{\text{largest value } - \text{smallest value }}{\text{number of classes}}\&=\dfrac{75-0}{{8}}\&\approx 9.375\&=10 (\text{rounding up})\end{align*}\] 

Now, if you count up the number of classes in the table, notice there is 11 different classes.  Why is there 11 when Number of Classes is set to 10?  Sometimes, the largest value of the data set gets counted in the last classes when it should not be.  It is a quirk of how GeoGebra defined class frequencies. (And there is nothing wrong with that the method GeoGebra uses; it is just uses a slightly different definition of boundary points than was given above.)  To correct for this difference, the Frequency Distribution Tool automatically adds an extra class by default.  But, notice that the last class has a frequency of 0. That means the extra class wasn't needed, and we can click on the click on the Deselect if Last Row Equals 0 checkbox to remove it. Therefore, we get the following frequency distribution.

Interpretation

The classes/bins column gives the range of values for each class, always including the first number in the range and excluding the last number in the range.  For example, the interval 0 to 9 means the range of values starting at 0 and include all the numbers up to but not including 10.  The Frequency, as before, tells us the number of years whose number of deaths fell into that range of values.  For example, there were 64 years that had 0 up to 10 deaths.

What is the Use Interval Notation Checkbox?

Some instructors/websites prefer to use interval notation to describe the classes/bins.  For example, 0 to 9 would be written as $[0,10)$ since $[0$ indicates to start and include 0 and $10)$ means to include all the number up to but not including 10.  When the check box is clicked, the frequency distribution looks like this.

For future examples, we will not use interval notation.

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The data from should already be loaded into GeoGebra.  If it is not, follow the steps at the beginning of to load the data in and selected option B from the dropbox.  Your tool should like this if you've been doing all the examples in order on this page:

All we need to do enter 7 for the Lower Class Boundary and 8 for the Class Width.  Notice the Number of Classes will update to 10 since   Since we want 8 classes, we will enter that value info class width.  Notice that the number of classes will update to 10 since \[\begin{align*}\text{number of classes}&= \dfrac{\text{largest value } - \text{smallest value }}{\text{class width}}\&=\dfrac{75-0}{{6}}\&\approx 12.5\&=13 (\text{rounding up})\end{align*}\]