maths skills Flashcards
what does standard deviation measure?
variation or spread of data about the mean
what is standard deviation a measure of?
precision of data
what does a low standard deviation indicate?
data have narrow range
points are grouped closely to the mean
greater precision
greater validity
increased confidence in data
what does a high standard deviation indicate?
data have large range
points are not well-grouped
lower precision
lower validity
decreased confidence in data
what do the symbols in the equation for standard deviation represent
s= standard deviation
∑=sum of
x=value in data set
x̄=mean of data set
n= number of values in data set
how to comment on standard deviation and precision of a data set?
higher/lower standard deviation with figures
values vary more/less about the mean
greater/smaller precision
magnification equation
magnification= image size/ actual size
what are unpaired t-tests used for?
comparing whether there is a significant difference between 2 means
why is the unpaired t-test unpaired?
the data was obtained from 2 different organisms
unpaired t-test steps
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?
what do the symbols in the unpaired t-test represent?
x̄=mean of data set
S=standard deviation
S^2=variance
N=number of values in set
|=modulus, makes value positive
how to calculate degrees of freedom for an unpaired t-test?
sample size- number of data sets
when are paired t-tests used?
when 2 sets of measurements are taken from the SAME organism
what do the different symbols in the equation for the paired t-test represent?
đ=mean difference
n=number of pairs of data
sd=standard deviation of the differences
paired t-test step by step
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
how to work out degrees of freedom for a paired t-test?
n-1
what is spearman’s rank correlation coefficient used for?
consider relationships between 2 sets of data
tells us whether 2 data sets are correlated or not, and whether that correlation is significant
what do the symbols in the equation for spearman’s RCC represent?
∑=sum of
D=difference between the ranks
n=number of pairs of data
range of spearman’s RCC?
value must be between -1 and 1
order of ranking for spearman’s RCC?
rank from largest (1) to smallest
how do you rank for spearman’s RCC if two or more values are the same?
they must take the same rank so do the mean of the ranks which the values cover
circumference of circle equation
2πr
area of circle equation
πr^2
surface area of a cuboid equation
2(bh+bl+hl)
volume of cuboid equation
hbl
percentage change equation
percentage yield equation
percentage error (uncertainty) equation
(2x absolute uncertainty)/quantity measured x100
Rf value equation
distance moved by solute/ distance moved by solvent
rate equation
change in quantity/ time taken
what format do you write a ratio in
x:1
how to increase confidence in data
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
tips describing graph
split into 2/3 sections
use data
process data
