Continuous and Discrete Data

If a 500 g bag of sweets contains 7 sweets, then the discrete data in this scenario would be the number of sweets as it is a countable value, whereas the weight of the bag would be continuous data as it is a value that you measure.

A box of 10 books is placed on a scale. The scale reads 8 kg. Identify the discrete and continuous data in this situation.

Solution

The number of books in the box is the discrete data. The exact number of books would have been determined by counting them, hence why it's discrete data.

The weight of the box is continuous data, as its value of 8 kg was measured using a scale.

A sprinter takes 17.2 s to run 100 m at a speed of 21 km/h. Identify the data in this situation.

Solution

The time of 17.2 seconds is continuous data.

The speed at which the sprinter runs is also continuous data.

You are asked to record your classmate's heights and present a summary of the results to your principal. One way of doing this would be to list each student's height next to their name, but an easier way of showing this could be to represent it by choosing ranges of heights and listing the number of students that fall within each range.

The ranges you decide on are as follows:

\[ \begin{align} &150 - 159\text{ cm} \\ &160 - 169\text{ cm} \\ &170 - 179\text{ cm} \\ &180\text{ cm}+ \end{align}\]

After measuring each of your 15 classmates and making a mark next to each range they fall within, you tally the results to get:

This is grouped data as you have grouped all the students who fall within a specific interval together instead of representing each of their heights individually.

Please note that the number of students that fall within each interval is discrete data, but their heights are still considered to be continuous data.

A class of 20 students was asked to raise their hands when their favourite subject was called. The teacher counted five hands for Mathematics, seven hands for biology, two hands for geography and six hands for chemistry.

The teacher decided that the best way to visualize the data was to make use of a bar graph, so she made the following:

Fig. 1. Bar graph showing students favourite subjects.

As you can see, there are multiple values that the teacher counted. Each one of these is of the discrete data type. Each bar on the graph represents a subject, and the top of each bar coincides with the number of students, as shown on the y-axis.

Your teacher asks you to collect a set of continuous data and represent it in a graph. You decide to record the temperature at 9am every day for a week, using the thermometer in your geography classroom.

You record the following values:

To represent this data, you could choose a line graph:

Fig. 2. Line graph showing the temperatures recorded on each day of the week.

The shape of the graphs helps show how the temperature varies throughout the week.

Alternatively, you could choose to represent the data with a scatter plot and a line of best fit:

Fig. 3. Scatter plot showing the temperature recorded on each day of a week.

As shown in the diagram, a line of best fit can be used to see if there is any linear correlation between the data.

Using the same values as from the previous example, you can represent the temperatures using a bar graph:

Fig. 4. Bar graph showing the temperatures recorded on each day of the week.

Following on from the heights example in the grouped data section above, you can plot a graph of the results.

Remember that these were the heights you recorded:

The easiest way to show this spread of data would be to use a histogram.

Using the \(x\)-axis to represent the range of heights and the \(y\)-axis to represent the number of students, you will end up with a histogram that looks like the following:

Fig. 5. Histogram showing the heights of the students in a class.

Alternatively, you could represent the data using a cumulative frequency graph:

Fig. 6. Cumulative frequency graph showing the heights of the students in a class.

You and your family want to go to a trampoline park, but you all need special socks to be allowed to jump. The socks only come in the following sizes:

• Size A - fits shoe sizes 1-3
• Size B - fits shoe sizes 4-6
• Size C - fits shoes sizes 7-9
• Size D - fits shoe sizes 10-12

Your mother tasks you with collecting the shoes sizes of each family member and tallying the total number of pairs of socks needed per size. Anybody who wears half sizes must take the next size up. She is also a school teacher and asks you to represent this data in a graph as well for extra practice for your upcoming exams.

First, you show the data in a table:

Next, you draw a histogram to represent the data:

Fig. 7. Histogram showing the shoe sizes and pairs of socks needed for each member of a family.