Representing Simple Discrete data

We will learn some relevant concepts using a simple example. 15 students took a 5-question test that required either true or false as answers.
The scores could be:
2 1 3 4 4 3 3 4 3 5 4 4 5 4 4

We could first tally the results.
Number of Correct Answers. Frequency
1 /
2 /
3 ////
4 //
5 //

The data could also be arranged into a table called frequency distribution/table.
Number of Correct Answers 0 1 2 3 4 5
Frequency 0 1 1 4 7 2

Next, we could also represent this data graphically using a bar chart.

Mode is the observation value that occur with the largest frequency. In our example above, the mode is 4.

Use of GDC.
[STAT] Select 1:EDIT [ENTER]
{Enter your data x into the column under L1 and frequencies into another column under L2}

Once finished then press [2nd][MODE] for quit. Before you plot your histogram, make sure there is no function in [Y=] because they will interfere with your plot latter.
[2nd][Y=] select 1:Plot1 to activate the plot by selecting ON [ENTER]. Then move your cursor to the Type and select the icon with bars and [ENTER]. Make sure that the Xlist and Freq(frequency) correspond to your respectively lists. If not, make the appropriate changes.

Before you plot, make sure that you set your [WINDOW] to match your data. In the example above, we could have Xmin=-1, Xmax=7, Xscl=1,Ymin=-0.5, Ymax=8,Yscl=1,Xres=1.
This setting will leave some to the left and right of the histogram.
[Graph] to plot the histogram. Press [TRACE] and appropriate arrow buttons to read these bars.

This histogram can help you to draw an accurate histogram or sketch a quick histogram as part of your workings.


A group of teachers had been surveyed about their daily consumption of coffee (measured in cups). The frequency distribution is as below:
Number of cups 1 2 3 4 5
Frequency 7 3 5 0 1


  1. Represent the above data with a bar chart.
  2. How many teachers had been surveyed?
  3. What is the mode in this frequency distribution?

The shape of a distribution

The example here is a distribution that is negatively skewed. That is there is a long tail at the lower (negative) end of the distribution.

The distribution is positively skewed if there is along tail at the high (positive) end of the distribution. Here, we have a distribution represented by a vertical line graph.


If all the bars are of the same height then we have a uniform or rectangular distribution.
If the shape of the distribution is symmetric and bell-shaped then it is known as a normal distribution.