# 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.
0
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. • The height of the bar reflects the frequency.
• All the bars have the same width and they are labelled in the middle of the bar on the horizontal axis to convey the message that these are discrete data.
• Alternatively, one can replace the bar by a vertical line. In this case, we obtained the vertical line graph. The vertical lines are distinct lines and reinforce the discrete nature of these data.
• The sum of these frequencies is the total number of students surveyed.

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

Exploration:
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

Questions:

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.