maths skills

Question 1

what does standard deviation measure?

Answer 1

variation or spread of data about the mean

Question 2

what is standard deviation a measure of?

Answer 2

precision of data

Question 3

what does a low standard deviation indicate?

Answer 3

data have narrow range
points are grouped closely to the mean
greater precision
greater validity
increased confidence in data

Question 4

what does a high standard deviation indicate?

Answer 4

data have large range
points are not well-grouped
lower precision
lower validity
decreased confidence in data

Question 5

what do the symbols in the equation for standard deviation represent

Answer 5

s= standard deviation
∑=sum of
x=value in data set
x̄=mean of data set
n= number of values in data set

Question 6

how to comment on standard deviation and precision of a data set?

Answer 6

higher/lower standard deviation with figures
values vary more/less about the mean
greater/smaller precision

Question 7

magnification equation

Answer 7

magnification= image size/ actual size

Question 8

what are unpaired t-tests used for?

Answer 8

comparing whether there is a significant difference between 2 means

Question 9

why is the unpaired t-test unpaired?

Answer 9

the data was obtained from 2 different organisms

Question 10

unpaired t-test steps

Answer 10

1)state null hypothesis that there is no significant difference between the means (test will tell us to accept or reject it)
2)use data to calculate value for t
3)work out degrees of freedom
4)use critical values table and look at 5% first
5)conclude: is there a significant difference?

Question 11

what do the symbols in the unpaired t-test represent?

Answer 11

x̄=mean of data set
S=standard deviation
S^2=variance
N=number of values in set

|=modulus, makes value positive

Question 12

how to calculate degrees of freedom for an unpaired t-test?

Answer 12

sample size- number of data sets

Question 13

when are paired t-tests used?

Answer 13

when 2 sets of measurements are taken from the SAME organism

Question 14

what do the different symbols in the equation for the paired t-test represent?

Answer 14

đ=mean difference
n=number of pairs of data
sd=standard deviation of the differences

Question 15

paired t-test step by step

Answer 15

1)state null hypothesis
2)work out difference between pairs
3)work out standard deviation of the differences
4)calculate value for t
5)work out degrees of freedom
6)use critical values table to see if there is a significant difference

Question 16

how to work out degrees of freedom for a paired t-test?

Answer 16

n-1

Question 17

what is spearman’s rank correlation coefficient used for?

Answer 17

consider relationships between 2 sets of data
tells us whether 2 data sets are correlated or not, and whether that correlation is significant

Question 18

what do the symbols in the equation for spearman’s RCC represent?

Answer 18

∑=sum of
D=difference between the ranks
n=number of pairs of data

Question 19

range of spearman’s RCC?

Answer 19

value must be between -1 and 1

Question 20

order of ranking for spearman’s RCC?

Answer 20

rank from largest (1) to smallest

Question 21

how do you rank for spearman’s RCC if two or more values are the same?

Answer 21

they must take the same rank so do the mean of the ranks which the values cover

Question 22

circumference of circle equation

Answer 22

2πr

Question 23

area of circle equation

Answer 23

πr^2

Question 24

surface area of a cuboid equation

Answer 24

2(bh+bl+hl)

Question 25

volume of cuboid equation

Answer 25

hbl

Question 26

percentage change equation

Answer 26

Question 27

percentage yield equation

Answer 27

Question 28

percentage error (uncertainty) equation

Answer 28

(2x absolute uncertainty)/quantity measured x100

Question 29

Rf value equation

Answer 29

distance moved by solute/ distance moved by solvent

Question 30

rate equation

Answer 30

change in quantity/ time taken

Question 31

what format do you write a ratio in

Answer 31

x:1

Question 32

how to increase confidence in data

Answer 32

increase no. of repeats at each temp, which enables identification of anomalies. if anomalies are present, take more repeats and dilute effect of the anomalies to make a more accurate mean, increasing reliability
calculate standard deviation ad add error bars to mean points on graph. if range is > 10% from mean, less confidence
perform statistical test (e.g. unpaired t-test) to assess the significance of the difference between the means at different temperatures

Question 33

tips describing graph

Answer 33

split into 2/3 sections
use data
process data