Free Software to Plot Histogram & Frequency Polygon on Graph Paper

usING the software to Plot a Histogram & Frequency Polygon on Graph Paper

Step 1: Insert the frequency table.

Insert the frequency table in the table input provided. Each row corresponds to a class and thus will be represented by a bar in the histogram. Note that the upper boundary of a class must be equal to the lower boundary of the next class. This ensures that the histogram has all its bars touching. In the default example provided, the upper boundary of the first class is 5 which is equal to the lower boundary of the second class (which is also 5). The input table accepts up to 15 classes (i.e. it has 15 rows). In case you have less than 15 classes, just leave the remaining rows blank.

Step 2: Set the standard width.

First of all, the class width is the difference between the upper boundary and the lower boundary. For example, the width of the first class is 5-1=4; the width of the second class is 10-5=5, and so on. In the case when all the classes have equal width, set the standard width to be equal to this unique width of the classes. In the case when not all the classes have equal width, set the standard width to be equal to any one of the class widths, for example the smallest class width or the largest class width or the most common class width. The software uses the standard width to make an adjustment to the heights of the histogram bars, incorporating the fact that not all the classes have equal width. The formula used is in fact:

    \begin{equation*}\textup{Estimated Frequency}=\frac{\textup{Standard Width}\times\textup{Frequency}}{\textup{Class Width}}\end{equation*}

where the estimated frequencies are the heights of the histogram bars. Note that in the default example, the standard width is set to be equal to 5 which happens to be the width of the second class.

Step 3: Set the x-axis scaling.

In the usual graph paper, 5 tiny boxes correspond to 1 cm.  Here you decide how many units of the x variable you would like to put in 1 cm (i.e. in 5 tiny boxes). In the default example, the x-axis scaling is set to be equal to 1, that is, every 5 tiny boxes (a centimeter) represents 1 units of the x variable. Note that if you change the x-axis scaling to 2, then every 5 tiny boxes will represent 2 units of the x variable and thus the width of the histogram will be smaller (actually half of the width of the default histogram).

Step 4: Set the y-axis scaling.

Set the scaling of y-axis in the same way as described in Step 3 for the x-axis.

Step 5: Set the title, x-axis, y-axis labels.

Customise the histogram title and the labelling of the x and y axis.

Step 6: Add a Frequency Polygon to the Histogram Chart.

Click the tick box if you would like to add the Frequency Polygon on top of the histogram chart.

Step 7: Change the aesthetics of the plot.

One could change the colour of the graph paper grid, the colour of the bars of the histogram and also the colour of the frequency polygon. Play around with the colours in order to get good contrasts in order to communicate your statistics clearly.

UnDERSTANDING THE OUTPUT OF THE HISTOGram & Frequency Polygon Software

Frequency Table Statistics

The software first outputs a table with some information about the classes. In particular, the class width is the difference between the class upper boundary and the class lower boundary. The class mark is the average of the lower and upper boundary of the class. It represents the midpoint of the histogram bars and is used in order to draw the frequency polygon. The estimated frequency represents the heights of the histogram bars after an adjustment for unequal class widths.

Histogram & Frequency Polygon plot on graph paper

The software displays a preview of the histogram and frequency plot on a graph paper which is not full-sized. Click on the “Download Plot” button in order to download an image file of the full-sized plot on your device.