Maths for A Level Biology - updated edition

2.1.3 Per cent frequency Environmetal gradients can be assessed by measuring the per cent frequency of a plant along a transect. This can be done in two ways: a) Point frame quadrat: this is a metal bar 0.5m long with 10 holes, 10 cm apart. It is supported just above the transect, at intervals along it, at 90° to the line. At each distance along the transect, a needle is slotted vertically down through each of the 10 holes on to the plants below. If the needle touches the species in question, the species is scored. The number of times out of 10 a species is touched allows an easy calculation of percentage frequency at each position along the transect. The percentage frequency is the frequency of the plant species occurring out of 10 samples. If a daisy is touched with the needle in 4 positions at, say, 10m along the transect, then we can say that the percentage frequency of daisies at 10m is 4 10 × 100 = 40%. b) Gridded quadrat: a square frame quadrat may be divided into a 10 × 10 grid, giving 100 squares. The quadrat is laid down along the transect and at each position, the numer of squares in which the plant species occurs is counted. The number of squares containing the plant, out of 100, gives the percentage frequency. It can be done with a 5 × 5 grid, but then, as there are only 25 squares, each represents 100 25 = 4% of the total. The number of squares containing the plant is multiplied by 4 to give the percentage frequency. Smaller squares give a more accurate estimate. 2.1.4 Per cent area cover Quadrats can be used to estimate the percentage area covered by a plant species, and this is discussed on pages 75–76. 2.1.5 Percentage error An error, in this context, does not mean a mistake. It refers to the uncertainty in a measurement related to the size of the calibration on the measuring equipment. Such an error occurs for every reading in an experiment and so it is described as a systematic error. If, for example, the smallest graduations on a ruler are at 1mm intervals, when a length is measured, there is an uncertainty at each end of the scale of up to 0.5mm. The measurement of length can, therefore, only be accurate to +1mm, i.e. 0.5mm at each end. The percentage error is affected by: ▪ The size of the graduation: a smaller graduation gives more accurate reading and reduces uncertainty. ▪ The size of the measurement: the uncertainty is proportionally smaller with a larger reading than with a smaller reading. The percentage error, or uncertainty, can be calculated: Example 1 8.6 cm 3 water was measured with a 10 cm 3 syringe, calibrated to 1 cm 3 . % error = accuracy measured length × 100 = 1 8.6 × 100 = 11.6 % (1 dp) QUICKFIRE 2.3 On developing iron-deficiency anaemia, a girl’s red blood cell count changed from 7500000 /mm 3 to 5100000 /mm 3 . Calculate the percentage change in her red blood cell count. Point frame quadrat Pointer Errors related to the scale on a piece of apparatus are systematic and affect all the readings in an experiment. Their influence can be calculated. It is hard to take measurements in exactly the same way twice, so random errors occur. They are statistical fluctuations in the data. Mathematics for Biology 34