Pictograms

In a pictogram, a symbol/icon is used to represent a quantity of items, and a key is included to explain what each symbol/icon represents. 
However, a pictogram is not a very accurate method of representing exact data. It only gives a quick comparison of the relative number of each type of item. 

Bar Graphs

1. A bar graph represents data by using rectangular bars of equal width.
2. The bars can be drawn vertically or horizontally.
3. The height/length of each bar is proportional to the data represented.
4. The spaces between the bars are uniform.

Pie Charts

A pie chart displays the given data using sectors of a circle. The angle in each sector is proportional to the number of items represented.

Line Graphs

A line graph is drawn by plotting the points corresponding to the data and then joining the points with line segments.

Frequency Tables and Histograms

Frequency Tables
1. A frequency table shows how often a value occurs.
2. The number of times a value occurs is called its frequency.

Histograms
1. A histogram is a vertical bar graph with no gaps in between the bars.
2. The area of each bar is proportional to the frequency it represents.
3. We can use a histogram to display the information given in a frequency table.

Grouped Frequency Table
In a grouped frequency table, the data are grouped into class intervals of equal sizes. 

Dot Diagrams

A dot diagram is drawn by placing dots that represent the values of a set of data above a horizontal number line. The number of dots above each value indicates how many times the value occurred.

Stem and Leaf Diagrams

In a stem and leaf diagram, each value is split into two parts, the stem and the leaf, by a vertical line. The following video teaches you how to plot stem and leaf diagrams:

Mode, Median and Mean

The mode, median and mran are measures of central tendency. A measure of central tendency is a single value that describes where the data are centred, i.e. its average value.

Mode
1. The mode of a set of data is the value that occurs most frequently.
2. In some distributions, no value appears more than once so there is no mode. In other distributions, there may be more than one mode.
Note: The class interval with the highest frequency is called the modal class.

For example, in the following set of data, the mode is 7.
1, 1, 2, 6, 7, 7, 7, 8, 9

Median
1. The value exactly in the middle of a set of ordered numbers (ascending or descending) is the median.
2. To find the median of a set of n data:
- arrange the numbers in ascending order
- if n is odd, the median is the middle value. If n is even, the median is the mean of the two middle values. 
3. To find the middle position of a set of n data, use (n+1)/2.

For example, in the following set of data, the median is 5.5
1, 4, 5, 6, 8, 9

Mean
The mean of a set of data is obtained by dividing the sum of all the data by the total number of data.
The principle is the same when calculating mean for grouped data.

For example, in the following set of data, the mean is 5.
8, 3, 1, 2, 6, 7, 5, 5, 4, 9

Standard Deviation (Ungrouped Data)

The standard deviation, S, measures the spread of a set of data from the mean. 

Note:
- A smaller spread has a smaller standard deviation.
- A wider spread has a higher standard deviation.
- Standard deviation is always greater or equal to zero.

Standard Deviation (Grouped Data)

Worked Example

The following video is a worked example of how standard deviation can be found from frequency tables: