10/19 Mean, Median, Mode
The arithmetic mean is the standard average, often simply called the 'mean'. It is often confused with the median (the middle value) and the mode (the most occurring or likely value).
The mean is the arithmetic average of a set of values, or distribution. However, for skewed distributions, the mean is not necessarily the same as the middle value (median), or the most likely (mode).
For example, mean income is skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the level at which half the population is below and half is above. The mode income is the most likely income, and favours the larger number of people with lower incomes. The median or mode are often more intuitive measures of such data.
Mean
To calculate the arithmetic mean add up all the data, and then divide this total by the number of values in the data. For example seven students are timed whilst searching for information on the Internet. What is the arithmetic mean time taken to search?
2 minutes + 2 minutes + 3 minutes + 5 minutes + 5 minutes + 7 minutes + 8 minutes = 32 minutes
There are 7 values, so you divide the total by 7:
32 ÷ 7 = Artimetic mean = 4.57 minutes (to 2 decimal places).
Median
The median time taken to search calculated by putting the values in order, then find the middle value. If there are two values in the middle then you find the mean of these two values, so:
2 , 2 , 3 , (5) , 5 , 7 , 8
The middle value is marked in brackets, and it is 5. So the median is 5 .
Mode
The mode time taken to search is the value which appears the most often in the data. It is possible to have more than one mode if there is more than one value which appears the most. So:
2 , 2 , 3 , 5 , 5 , 7 , 8
The values which appear most often are 2 and 5. They both appear more time than any of the other data values. So the modes are 2 and 5 .
The Range
To find the range, you first need to find the lowest and highest values in the data. The range is found by subtracting the lowest value from the highest value.
The data values: 2 , 2 , 3 , 5 , 5 , 7 , 8
The lowest value is 2 and the highest value is 8. Subtracting the lowest from the highest gives: 8 - 2 = 6. So the range is 6 .
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