limpets can be found on bare rock

8/14/2019 Limpets Can Be Found on Bare Rock

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Variation


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Limpets can befound on bare

rock

or under

seaweed


3/20

All the limpets are of the same

species. Do you expect anydifferences between the twogroups?

Yes, because No, because


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15 limpets from each habitat were

measured along their longest sides


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Limpets on bare rock

30.4025.1019.0025.20

22.4023.6017.8011.9016.6030.80

22.7033.8025.5026.7024.60

mean: 23.74

longest side of

limpet /mm


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Limpets under seaweed

18.9017.4027.1038.4044.0021.1029.3016.3013.50

19.004.907.3010.9012.7011.50

Mean:19.49

longest side oflimpet /mm


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The two mean values suggest thatthe limpets on the bare rock arelarger than the limpets under the

seaweed. Can we justify this

conclusion? Yes, because No, because


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Displaying the data as a graph canhelp to see patterns


9/20

Frequency distribution graph for size of limpe ts on ba

0

1

2

3

4

5

6

0.0 -

4.9

5.0-

9.9

10.0-

14.9

15.0-

19.9

20.0-

24.9

25.0-

29.9

30.0-

34.9

35.0 -

39.9

40.0-

44.9

Frequency distribution graph for size of limpets under

seaweed

0

1

1

2

23

3

4

4

5

0.0 - 4.9 5.0-9.9 10.0-

14.9

15.0-

19.9

20.0-

24.9

25.0-

29.9

30.0-

34.9

35.0 -

39.9

40.0-

44.9

What extrainformationdo you get

from thegraphs?


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Standard deviation

In each sample, the data varies about themean. We need some way of quantifyingthis variation so that we can see whetherthe means are truly different or whetherthe differences are just due to chancehappenings when the samples were being

taken. Standard deviation is a measure ofthe spread of data about the mean.


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Calculation of standard deviationLength of limpetx

x2

30.40 924.1625.10 630.01

19.00 361.00

25.20 635.04

22.40 501.76

23.60 556.96

17.80 316.84

11.90 141.61

16.60 275.56

30.80 948.64

22.70 515.2933.80 1142.44

25.50 650.25

26.70 712.89

24.60 605.16

366.10 8917.61

n =15

The standard deviationfor the limpets on barerock works out to 5.76.

The standard deviationfor limpets underseaweed works out to11.06.


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Standard deviation is as importantto A level as means are to GCSE

You will need to be able to use yourcalculator to find out the standarddeviation of a set of data.

Different calculators do this in slightlydifferent ways.

Whenever you have a number of differentdata points, always work out theirstandard deviation as well as their mean


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Find out how to calculate standarddeviation using your calculator

Switch it on Press MODE until it offers SD Press the number that is under SD

(clear the memory: this is different for each calculator;look in the lid for instructions) Enter the data, in the way the instructions tell you. You can then find mean and standard deviation from

the instructions on the lid.


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DONT PANIC!

You wont have to do this on your ownuntil you do the A2 coursework, but bythen it is assumed that it has become an

automatic part of your approach to data.


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These are the mean values, plotted as a barchart. Are the two samples really different or

is the difference due to chance?mean length/mm

0

5

10

15

20

25

on bare rock under seaweed


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We can use the standard deviationto answer this question.

The standard deviation, divided by thesquare root of the sample size, gives anumber called the standard error.

s.e. = s.d

n

The standard error x 2, when added toand subtracted from the mean, generatesconfidence limits.


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Standard deviation = 5.76,

so standard error = 5.76/15 = 1.49

The mean of this sample was 23.74,so the confidence limits are

23.74 + (1.96 x 1.49)

and 23.74 (1.96 x 1.49).These come to 26.66 and 20.82

For limpets on bare rocks,


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Doing the same calculation for the limpetsunder the seaweed, the confidence limitswork out to 25.1 and 13.88


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These are the limits within which 95% of thedata will lie.

You then draw these limits on the graph,you can find out if they overlap. If they do,you can be 95% confident that your twosamples come from the same population, ie

any difference between them is due tochance, not real variation. If they do notoverlap, you can be 95% confident that theyare from different populations where the

differences are due to factors other thanchance.


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limpets can be found on bare rock

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