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STATISTICS

ALL YOU NEED TO KNOW ABOUT STATS

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STATISTICAL MEASURES

MEASURES OF SPREAD

Frequency Diagrams:

When you have a group of data, a frequency table is created in order to find the number of times, or the FREQUENCY, of the occurrence of these numbers. If you have a very large amount of data, it can be grouped into smaller sections (categories or classes) and the frequency of each section is noted as the amount of single data items which fall within this group.

For example: The following figures are the heights (in cm) of a group of students:

156 172 168 153 170 160 170 156 160 160 172 174

150 160 163 152 157 158 162 154 159 163 157 160

153 154 152 155 150 150 152 152 154 151 151 154

Since there are a large number of different heights, it is a good idea to group the height data into the sections (categories) 148-150, 151-153, 154-156 .... before counting the frequencies in each section.

HEIGHTS----------FREQUENCY

148-150--------------3

151-153--------------8

154-156--------------7

157-159--------------4

160-162--------------6

163-165--------------2

166-168--------------1

169-171--------------2

172-174--------------3

The total of the frequency column should equal the count of the number of data items (36 data items in this case).

Now the objective is to show the distribution of the data as clearly as possible, and this can best be seen graphically. There are many ways to show the distribution.

The HISTOGRAM:

Note: 1) It is the AREA of the bars, not their height, that represents the number of data items in each category (section).

You can also show the same data using a line graph.

USING A GRAPHING CALCULATOR:

To enter the original data into your calculator:

Press STAT and choose EDIT from the screen menus. if necessary, press 4 followed by the keys L1 (2nd 1), L2 (2nd 2) etc. ENTER to clear any previous lists. Next select STAT EDIT. the data can now be entered as a column under L1.

The data can now be expressed as a statistical graph. as with other types of graphs, the appropriate window must be set. in the present case, the X data range should be set at 145-175 the Xscl setting determines the width of the class interval that will be used.

Next, any cartesian graphs need to be cleared. press Y= and clear any rule that you see. The statistical plotting facility must now be activated. Press 2nd STAT PLOT. Choose plot 1 and turn it on by using the arrows to the word ON and then press ENTER. Also select the histogram symbol from kthe list of available plot types. We entered the data as L1 so we must select this as the source of data. because each height was ene\tered separately, the frequency must be defined as 1. Pressing GRAPH will display the histogram.

if the data is presented as a grouped list (frequency table), the X values should be entered as L1 and the frequencies as L2. In the case of height data, the mid-point of each class interval (149, 152, 155, etc.) should be entered in L1. the STAT PLOT instructions must also be set to record the fact that the frequencies are stored in L2 before statistical plots or calculations can be successful.