A measure of central tendency is a number which indicates the middle of the distribution of data values. The three main measures are the median, the mode and the mean.

6, 6.7, 3.8, 7, 5.8

Arranged in order of magnitude these are

Eg.2 The first 6 Commodore prices in $,000 are

6, 6.7, 3.8, 7, 5.8, 9.975

Arranged in order of magnitude these are:

For all Commodores there are n = 38 values, so the middle ones are 19th and 20th values (so that there are 18 on either side). The 19th and 20th values are both $9,500 so the median is $9,500.

The MINITAB command for obtaining the median of a data set stored in column C1 is

MTB> median c1 MEDIAN = 9500.0

where *n* is the total number of values

e.g. for the Commodore prices

The MINITAB command is MEAN C1. Also the mean and other summary values are given by DESCRIBE C1

Data set A: 2,3,3,4,5,7,8

Data set B: 2,3,3,4,5,8,20

Both have n = 7 values.

It is necessary to sort the data in order of magnitude before you can find the median. For large data sets this may be time consuming and this is the reason why medians were not used much until computers became readily available.

In many situations the median is a better description of central tendency (e.g. many more people have less than the average income than have more).

## APPLET "Centres"Click and drag below the line to add and move data. Drag points above the line to remove them. Which is the mean and which the median? Which is more responsive as you move (a) the middle point (b) an end point? In a real dataset, which (middle or end) is more likely to be a data error? |

The median for grouped data is calculated as the midpoint of the class interval that comes closest to having half the values above and below it.

(or 18.75 + 0.5 years if we use the mid-point interval)

For grouped data like the Commodore
prices take the x-values as interval mid-points

e.g. for
interval 2000-4999 use , etc
then

(which is close to the mean calculated from the individual values, 10080)

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