 # Averages

In science we are often working at the limits of our measuring tools or experimental techniques. In order to have confidence in their findings scientists will repeat results. The variation in the repeat measurements enables them to identify the range within which the true value probably lies.

A result is said to be reliable if it is replicated on different occasions and preferably by different people.

The average of a group of measurements can be calculated in three ways – mean, mode or median. The way to be used in each case depends on the type of measurements in the group.

#### Mean

Used when measurements are true numbers which can be divided into one another – length, weight, temperature, speed, concentration of a solution – calculated by adding the measurements together and dividing by the total number of measurements.

Scientists use means a lot to average repeated results but... they can be easily distorted by freak results.

##### Global warming ? The table shows the average temperature variation in the lower atmosphere each year from 1988 to 2000 in oC.

 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 0.12 -0.08 0.1 0.1 -0.22 -0.2 -0.06 0.1 -0.01 0.01 0.46 -0.03 -0.04

The ten year mean average calculated from 1988 to 1997 is -.015 yet the unusually high rise in the average temperature in 1998 causes the ten year mean to rise to 0.019 and the ten year means for 1999 and 2000 continue show a rise in temperature even though the average temperature has fallen in both of those years.

#### Median

Used when measurements are numbers that represent ranks or positions in a list. You calculate it by putting the numbers in numerical order and finding the middle one.

If 25 people are asked to rate how serious the threat of global warming is on a scale of one to five, we get the following results.

2, 3, 4, 4, 3, 4, 5, 2, 2, 3, 2, 5, 4, 3, 4, 3, 2, 3, 3, 5, 3, 2, 4, 4, 3

Putting them in order gives

2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5

And the middle number or median is 3.

This method of calculating the average should always be used whenever the numbers being averaged are not in true ratio ie. you can’t guarantee that 4 divided by 2 will equal 2 because 4 represents ‘ strongly agree’ and 2 represents ‘agree a little’ or 4 represents fourth place and 2, second place and the intervals between places are not equal.

#### Mode

A simple measure that is used to find out which is the most frequently occurring result.

In the above example 3 occurs 9 times, twice more than any other number, so it is also the mode.

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