YHS+Year+9+Data+Representation+and+Analysis

//Statistics// is a branch of mathematics that deals with the collection, organisation and analysis of data. Statistical information is used by a large number of professions and organisations, icluding science, psychology, business and government departments.

Frequency distribution and cumulative frequency tables
A frequency distribution table is useful for organising and collating data. It shows (in the **frequency** column) how many times a piece of data (a **score**) has occurred.

Another column can be added to a frequency distribution table to create a **cumulative frequency** column. This extra column shows the progressive scores. The cumulative frequency of a given score is the number of scores less than or equal to that score. = = =Example: =

(Instruction: Paste in hand out and then draw up table below) (Instruction: Add in cumulative frequency column "on board")
 * ** Score (//x//) ** ||  ** Tally **  ||  ** Frequency (//f//) **  ||
 * 0  1   2   3   4   5   6   7  ||   ||   ||
 * ||  || Total ||

=Task: =

Frequency and cumulative frequency diagrams
There are two diagrams we can use to display frequency data and culmulative frequency data
 * frequency histogram - basically a column graph
 * frequency polygon - basically a line graph

(Instruction: Students to write these next notes beside the graph on board) (For histogram) Note the half unit space before the first column and after the last column. There is no need to start from zero on the horizontal axis. The scores are plotted along the horizontal axis. (For polygon) Join the points (dots) on the graph with straight lines.On either side of these lines end on the horizontal axis. (For the combined) Sometimes a frequency histogram and polygon are drawn on the same axes. It is best to draw them using different colours to remind you they are seperate graphs. A **cumulative frequency** histogram and polygon are different in three ways:
 * the data is taken from the cumulative frequency column
 * the dots start on the horizontal axis on the side of the first column
 * the rest of thedots are on the right corner of each column instead of in the middle
 * the polygon does not return to the horizontal axis on the right

When a class test is out of 10, it is easy to write all the scores from 0 to 10 in a table. But what if the test score was out of 100? The table could end up very large. To overcome this problem, it is better to group the data. For example, if the test is out of 100, you can group the data as 0-10, 11-20, 21-30 and so on. These groups are called **classes**. The size of the classes depends on how many groups we would like to make.

Classes are also used for **continuous** data because they allow us to group a large number of possible values. For example, lengths can be groped as 1.00cm to 1.99cm, 2.00cm to 2.99cm and so on.

Classes do not overlap and, in general, they are of equal size. The **class centre** is the average of the two extreme scores in the class.

When we group data we lose some of the information. For eample, because we now do not know the individual scores, we cannot calculate the mean, median, mode and range exactly. However, approximate values for these statistics are generally just as useful.

Worked example
 * 48 || 39 || 69 || 80 || 40 || 67 || 20 || 92 || 49 || 33 ||
 * 56 || 58 || 31 || 54 || 35 || 24 || 85 || 14 || 42 || 77 ||
 * 52 || 26 || 64 || 43 || 59 || 72 || 79 || 57 || 99 || 21 ||
 * 37 || 29 || 74 || 51 || 60 || 62 || 3 || 46 || 53 || 63 ||
 * 41 || 89 || 65 || 34 || 52 || 68 || 61 || 82 || 25 || 45 ||