Science calculations

There are three different types of average which are all useful in science. They are called the mean, median and mode.

Mean

The mean is the most common type of average we use. To calculate the mean, add all the values together and divide by the total number of values.

Two students completed an ecological investigation into the dandelions on the school field. They randomly placed ten quadrats in shaded and sunny areas, in order to count the dandelions in each. Their results are below.

Quadrat number12345678910
Dandelions in shade4460142365
Dandelions in sun6678458553

The students wanted to compare their results, so they calculated the mean for each. They added up all the dandelions in the shade, which came to 35 and all those in the sun, which came to 56. They divided each of these numbers by ten to calculate the two means, as there were ten numbers from the ten quadrats.

Quadrat number12345678910TotalAverage
Dandelions in shade4460142365353.5
Dandelions in sun6678458553575.7

The number of dandelions per quadrat is given to one significant figure. Usually the same number of significant figures would be used in the results of a calculation, but giving the answer to two significant figures is acceptable in the case of finding the mean of a series of integers. Using three significant figures (eg 3.50) would be unacceptable as it would imply an inappropriate level of precision.

Median

To calculate the median, numbers are placed in increasing order of size. The median is the middle number in the list. The two students took an even number of readings, and they calculated the median as the mean of the two middle numbers.

The median for shade is four because both middle numbers are four and the median for sun is 5.5 as it is halfway between five and six.

Dandelions in shade0123444566
Dandelions in sun3455566788

Mode

The mode is the value that appears the most often. In the shade, the mode is four because there are three values of four. In the sun, it is five because there are three values of five.

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