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 you 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
Number of dandelions per quadrat in shade4460142365
Number of dandelions per quadrat in sun6578458553

The students wanted to compare their results, thus they calculated the mean for each. They added up all the dandelions in the shade, which came to 36 and all those in the sun which came to 57. They divided each of these numbers by ten to calculate the two means, as there were ten numbers from the ten quadrats.

Quadrat number12345678910TotalAverage
Number of dandelions per quadrat in shade5460142365353.5
Number of dandelions per quadrat 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 in this case when finding the mean of a series of integers, giving the answer to two significant figures is acceptable. Using three significant figures (eg 3.50) would be unacceptable as an inappropriate level of precision is implied.

Median

To calculate the median, a set of 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.

Number of dandelions per quadrat in shade0123444566
Number of dandelions per quadrat 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.

Using fractions and percentages

Visit the BBC Bitesize maths pages to learn how to use fractions and percentages.

If you are asked to calculate an answer and it has lots of decimal places, don’t forget to use the same number of significant figures as the input value with the least number of significant figures.

Calculating a mean value is an exception as explained above. For example, in the tables above of dandelions in quadrats are given to whole numbers. There are 3, 4, 5, 6, 7 or 8 plants. So, the mean can be given to one decimal place. It is correctly calculated as 5.5.

Drawing graphs

When you are asked to draw a graph, it is important that you:

  1. Put the independent variable on the horizontal axis and the dependant variable on the vertical axis and remember, the value of the dependant variable depends on changes made to the independent one.
  2. Construct regular scales for the axes and remember that your graph must fill as much of the paper as it can.
  3. Label the axes appropriately and remember to use units if you are given them.
  4. Plot each point accurately as each one will be checked individually.
  5. Decide whether the origin should be used as a data point.
  6. Draw a line of best fit (which may be a curve).

Extracting information from charts and tables

It is important you can extract information from tables. The table below shows the number of birds seen in two gardens in one hour over five days.

Day 1Day 2Day 3Day 4Day 5
Garden A86545
Garden B1312No results
Question

On which day and in which garden were the most birds seen?

Day one in garden A

Question

On which days and in which gardens were the fewest birds seen?

Day 1 and 3 in garden B

Question

Calculate the mean value for each garden.

Garden A \frac{8 + 6 + 5 + 4 + 5}{5} = 5.6

Garden B \frac{1 + 3 + 1 + 2}{4} = 1.8

The results from systematic sampling using quadrats along a transect are shown in kite diagrams. The diagram below shows the number of grasses and dandelions along a transect.

Kite diagram showing grasses and dandelions over 25m. Grasses rise slightly and fall slightly over long period then rise and fall steeply to 25m. Dandelions rise steeply, then fall gradually to 20m.
Question

How far along the quadrat were the most dandelions observed?

5 metres

Question

Describe the presence of grasses along the transect.

The number of grasses increased after five metres, but reduced at both 10 and 15 metres. After this it increased to its maximum at 20 metres. No grasses were seen after this point.

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