Edexcel AS Statistics revision notes

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Statistics notes
When deciding data groups always start with the lowest value, then down round if necessary
to the nearest 5 or 2, then make sure no numbers are in the same category.
Stem and leaf Diagrams
Frequencies of data sets should be shown in brackets
If a data set is large, split the group and once you come to 5 move to the next, (universal)
For comparison you can branch out the leaves on the stem, by working backwards and
forwards, your key should reflect this.
Histograms
Used when there are gaps in data and the bars have no gaps(same numbers are adjacent)
For all histograms, imagine p-q is a data group, find and plot the lower bound of p and the
upper bound of q (endpoints).
To find the width of a bar compare both groups, for the height of a bar first work out what 1
is equal to and times it by F then divide by width
When the data intervals are equal, simply plot with x being data and y being frequency
When the data intervals are not equal, and you wish to plot the relative frequency density,
add three columns, class width, frequency density and
relative frequency density.eg.
Height 119.5-129.5 129.5-139.5 139.5-144.5 144.5-149.5 149.5-154.5 154.5-159.5 159.5-169.5 169.5-179.5
Frequency 60 80 50 93 77 67 72 54
Class width 10 10 5 5 5 5 10 10
Frequency density 6 8 10 18.6 15.4 13.4 7.2 5.4
RFD 0.011 0.014 0.018 0.034 0.028 0.024 0.013 0.010
Area under all bars=1.
To calculate a certain distribution in x, find the whole, midpoint or fractions of the groups
involved and add together. E.g to find the number of people with the heights 142cm-152cm,
notice this includes midpoint, whole and ¼, so 77 x 1/2, 67, 72 x ¼, so
38.5+67+18=123.5~124.
To calculate a distribution on a graph, add up all areas and divide this by the total freq., times
this by the f.d height and the subtraction of the two points e.g. (1333/133)*8*(90-75)
Averages
To find the median from a frequency table, F/2 (round up), then keep adding F until you
reach this number
To find the mean from a frequency table with no grouping, do XxF, do XF/F and for
grouped data, add two columns, mid-term and midtermxF then do midtermxF /F.

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Quartiles
Take the X and for the median position, X x ½, for upper quartile position X x ¾, for
lower quartile position, X x ¼ and for interquartile range, upper quartile-lower quartile.
Boxplots
Always add a cumulative
frequency column to data, use
this to find values that fall into
these numbers
Can be vertical or horizontal.
Fences are calculated by
Interquartile range x 1.…read more

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Variance and standard deviation
Variance is a measure of spread and the
average of the squared distances from the median, standard deviation
is the square root of variance, look at equations below:
X X midpoint F Fxmidpoi Fx(midpoint
2
nt )
For non-frequency table data For frequency
table data Where X= mean of data
Coding can be given or made up e.…read more

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Comparing distributions
Mention one measure of spread and
one measure of average or centre in
questions
Probability
Probability experiment: has outcomes that occur at random
Experimental probability: e.g. throwing a die 100 times, getting 5 14 times 14/100=0.14
Theoretical probability: if a fair die was thrown, P(getting 5)= 1/6= 0.1616...…read more

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Using the mean of x and y, quadrants can be found on a graph and are numbered
anticlockwise from the right, so correlation is positive if plots are in quadrants 1st and 3rd
Summary statistics are used to calculate PMCC;
Regression
This shows the strength of the correlation, below shows y on x (work backwards for x on y)
Regression line y=a+bx b=Sxy/Sxx a=y-bx
Interpolation: predictions made inside the range of data (reliable)
Extrapolation: predictions made outside the range (unreliable)
Anscombe's data proves that sometimes…read more

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For cumulative distribution function, anything over the scale=1, and
F(X)= accumulating the probabilities, the last should be 1 (use this to equate functions)
To find the probability of an x term not given, round down, if there is a whole number minus
form it the previous number's probability.…read more

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