Unit 5 Section 1 : Frequency Tables: Discrete Ungrouped Data

In this section we revise collecting data to produce vertical line graphs or pie charts.

Example

Step 1: Produce a frequency table:
This is a table showing the number of times each score appears.
For example, the score "5" appears 4 times, so the frequency of "5" is 4.
You can also use a tally when counting up the frequency of each item.

Step 2: Work out the angles for the pie chart:
There are 360° round a circle, and 30 pupils in the class.
To work out the angle for each pupil, you need to divide 360° by 30.
The angle for 1 pupil is 12°.

To work out the angle for a particular score, you need to multiply the number of pupils who got that score by 12°.
For example, the angle for the score "5" will be 48° because the frequency of "5" is 4, and 4×12° = 48°.
The workings for this example are shown in the table below:

Score	Frequency	Angle
1	1	1 × 12° = 12°
2	1	1 × 12° = 12°
3	3	3 × 12° = 36°
4	1	1 × 12° = 12°
5	4	4 × 12° = 48°
6	5	5 × 12° = 60°
7	6	6 × 12° = 72°
8	5	5 × 12° = 60°
9	3	3 × 12° = 36°
10	1	1 × 12° = 12°
Totals	30	360°

It's a good idea to check that your angles add up to 360°.

Step 3: Draw and label the pie chart:
Start with a circle, and draw a line from the centre to the top.
Then mark off each angle around the circle, and label the "pieces" of the "pie".
Don't forget to give the pie chart a title.
The final result should look like this:

Step 4: Draw the vertical line graph:
In a vertical line graph, the frequency always goes on the vertical axis.
The scores will be on the horizontal axis and there will be one vertical bar for each score.
The height of each score's vertical bar is given by the frequency of that score.
Don't forget to label both axes and give the graph a title.
The final result should look like this:

Practice Questions
Work out the answer to each of these questions then click on the button marked to see whether you are correct.

(a) Use the pie chart to complete this sentence: "Half the class scored more than ____ marks."

(b) Use the bar chart to work out which score occured the most often.

Exercises

Question 1
Mr. Rafiq runs a video library. Over a period of 3 days he notes how many
videos have been borrowed during each hour. His records are shown below:

1	1	2	1	3	3	4	1	4	1
2	3	3	2	4	2	3	2	3	2
1	1	3	4	2	4	3	3	2	3

Mr. Rafiq decides to put the data in a table so he can draw a pie chart:

Videos in the hour Frequency Pie chart angle 1 2 3 4 Total (d) What was the largest number of videos hired in any hour? videos (e) What was the least number of videos hired in any hour? videos (e) What was the most common number of videos hired in any hour? videos

(a) Use the data above to work out the frequency of each value. Enter the frequencies in the table, and fill in the total frequency. (b) Work out the pie chart angles for each value. Enter the angles in the table, and fill in the total of the angles. (c) Label the pieces in the pie chart below:

When you want to draw lines on a vertical line diagram in the questions below, click where you want the top of the line to be. If you want to change the height of the line, click at a different height on the same line. If you want to remove a line, click the square at the top of the line. You can practise this on the vertical line diagram in Question 3.

You may find it helpful to have some paper to do tally charts for some of these questions.

Question 6
A train company keeps a record of how many trains are late each day.
The data for January and February are shown in the table below:

January	February
1 0 2 7 3 1 2 4 5 1 2 4 7 4 3 0 1 4 1 3 2 1 2 3 4 5 6 0 1 2 9	5 1 4 4 2 4 3 6 8 3 3 6 3 5 5 7 4 4 4 5 4 4 3 5 6 8 9 4
(a) Use the data above to complete the vertical line diagrams below for January and February:

(b) In which month was a better service provided to passengers?
January February

(c) How many days had 7 or more trains late (over both months together)?