Cambridge International A Level Biology Revision Guide

Cambridge International A Level Biology
Number of lemons
5
4
3
2
modal class
median class
Normal distribution
Many sets of data produce a symmetrical pattern when
they are plotted as a frequency diagram. This is called a
normal distribution (Figure P2.5a).
The data in a frequency diagram can also be plotted
as a line graph (Figure P2.5b). lf the data show a normal
distribution, then this curve is completely symmetrical.
a
1
0 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140
Number of of individuals
Mass of lemons / g
Figure P2.4 Lemon mass data plotted as a histogram.
496
Range and interquartile range
We have already met the term range, in the context of the
range of the independent variable. It means exactly the
same thing when applied to the results – it is the spread
between the smallest number and the largest. For the
fruit masses, the range is from 57 g to 135 g.
The interquartile range is the range into which
the middle 50% of your data fall. For the fruits, we
had 40 fruits in total. One-quarter of 40 is ten. The ten
smallest fruits had masses between 57 g and 83 g. The ten
largest fruits had masses between 106 g and 135 g. The
interquartile range is therefore the range of mass shown
by the remaining 20 fruits, which is 84 g to 105 g. This
can also be expressed as 21 g, the difference between 105 g
and 84 g.
Why would we want to know the interquartile range?
It is sometimes useful if we want to compare two sets
of data. Imagine that you have collected another set of
fruits from a different tree, and want to compare the two
sets. By concentrating on the middle 50% of the range,
you eliminate the fruits with extreme masses at either
end of the range. Comparing the interquartile ranges
of both sets rather than comparing the complete ranges
may give you a better idea of how similar or different the
sets are.
b
Number of of individuals
Measurement
Measurement
Figure P2.5 Normal distribution curves shown as a frequency
diagram and b a line graph.
QUESTION
Measurement
Measurement
P2.4 In a perfect normal distribution curve, what will be the
relationship between the mean, median and mode?