Data Presentation - SS1 Mathematics Lesson Note

Frequency table

A frequency table shows the frequency of each event occurring in a given data set. Frequency simply means the number of times an event occurs.

Example 1 the percentage scores of 30 students in an algebra test is shown below. Construct a frequency table to represent the data.

\[99\]	\[78\]	\[45\]	\[67\]	\[23\]
\[55\]	\[67\]	\[99\]	\[23\]	\[10\]
\[45\]	\[87\]	\[45\]	\[100\]	\[67\]
\[99\]	\[23\]	\[55\]	\[73\]	\[87\]
\[10\]	\[87\]	\[45\]	\[87\]	\[67\]
\[87\]	\[45\]	\[87\]	\[87\]	\[56\]

Solution

Test Score	Frequency
100	1
99	3
87	7
78	1
73	1
67	4
56	1
55	2
45	5
23	3
10	2

\[total\ frequency\ (number\ of\ test\ score\ entires)\mathbf{\ }\sum f = 30\]

Bar Charts

Bar charts makes of rectangular bars whose lengths are proportional to the frequency of data points. The bar chart of the frequency distribution of test scores above is given below:

Example 2 The allotment of time in minutes per week for some of the school subjects in SS1 class is:

SUBJECT	MINUTES
English Language	80
Mathematics	120
Biology	160
Geography	120
Chemistry	120

Construct a bar chart to represent the above data.

Solution

Pie charts

Another way of representing data is via a circular chart called a pie chart. The area of each sector of the pie chart is proportional to the frequency of the event in the data set.

Example: Represent the allotment of time in minutes per week for some of the school subjects in SS1 in the example above in a pie chart.

Solution

\[area\ of\ the\ sector\ for\ each\ subject = \ \frac{time\ for\ subject}{total\ time} \times 360{^\circ}\]

\[English\ Language = \ \frac{80}{600} \times 360{^\circ} = 48{^\circ}\]

\[Mathematics = \ \frac{120}{600} \times 360{^\circ} = 72{^\circ}\]

\[Biology = \ \frac{160}{600} \times 360{^\circ} = 96{^\circ}\]

\[Geography = \ \frac{120}{600} \times 360{^\circ} = 72{^\circ}\]

\[Chemistry = \ \frac{120}{600} \times 360{^\circ} = 72{^\circ}\]