Cambridge International Mathematics

282 Analysis of discrete data (Chapter 13)

82 57 75 71 66 80 92 74 89 70

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4 a b c d e f

We can get a better understanding of a data set if we can locate themiddleorcentreof the data and get an

indication of itsspread. Knowing one of these without the other is often of little use.

THE MEAN

Themeanof a data set is the statistical name for the arithmetic average.

mean=

the sum of all data values

the number of data values

or x=

P

x

n

where

P

x is the sum of the data.

The mean gives us a single number which indicates a centre of the data set. It is not necessarily a member

of the data set.

For example, a mean test mark of67%tells us that there are several marks below67%and several above

it.67%is at the centre, but it does not mean that one of the students scored67%.

THE MEDIAN

Themedianis themiddle valueof an ordered data set.

An ordered data set is obtained by listing the data, usually from smallest to largest.

The median splits the data in halves. Half of the data are less than or equal to the median and half are

greater than or equal to it.

For example, if the median mark for a test is67%then you know that half the class scored less than or

equal to67%and half scored greater than or equal to67%.

For anodd numberof data, the median is one of the data.

For aneven numberof data, the median is the average of the two middle values and may not be one of the

original data.

C THE CENTRE OF A DISCRETE DATA SET [11.4]

There are that are used to measure the of a data set.

These are: the , the and the.

three statistics centre

mean median mode

Thirty high schools were surveyed to find out how many

Year 12 students there were at each school. The following

data was collected:

Construct a tally and frequency table for this data.

Draw a vertical bar chart to display the data.

How many schools have at least 80 Year 12 students?

What percentage of the schools have less than 70 Year 12 students?

Find the modal class for the data.

Describe the distribution of the data.

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y:\HAESE\IGCSE01\IG01_13\282IGCSE01_13.CDR Thursday, 16 October 2008 9:32:09 AM PETER