1.2.3 gradient: for every extra 1 in x,
you get an extra m in y
1.2.4 intercept: when x is zero,
y is expected to be c
1.3 Extrapolation
2 Summary Statistics
2.1 Standard Deviation
2.1.1 Variance
2.2 Mean
2.2.1 Estimate from Grouped Data
2.3 Median and Quantiles
2.3.1 n+1 for individual items,
just n for grouped data
2.3.2 Skew
2.3.2.1 Formal definition
Annotations:
for positive:
o (Q2-Q1) < (Q3-Q2), i.e. right side of box fatter
o OR mean > median > mode, i.e. the lump of the mode happens early on, then there's more spread on the positive side
o 3(mean - median) / sd
2.3.3 Outliers: 1.5xIQR away from quartiles
2.3.4 Interpolation
Annotations:
it's basically about how far through the relevant class our wanted figure is.:
(how many items into this group) / (frequency of this group) x class width + class lower bound
2.4 When Comparing Data,
USE YOUR ASS!
Annotations:
Comment on:
o averages (whichever is handy)
o spread (sd, iqr, range)
o skew
use proper statistical names for things, not just "average" or "spread"
3 Graphs and Charts
3.1 Stem and leaf
3.2 Histogram
3.3 Cumulative Frequency
3.3.1 Curve for continuous, "steps" for discrete
3.4 Box plots
4 Probability
4.1 Discrete Random Variables
4.1.1 Expectation and Variation
4.1.1.1 Expectation Algebra,
Var(aX+b), E(aX+b)
4.1.2 Cumulative Probability F(x)
4.1.3 simultaneous equations,
use sum of p = 1
4.2 Normal distribution
4.2.1 Two sketches every time
4.2.2 Mapping ("bridge") equation: z=(x-mu)/sd
4.2.2.1 if mean and sd missing, set
up two bridge equations
4.2.3 if you have a prob. or a
%, do reverse-lookup in
tables to get z value
4.3 Trees
4.4 Venn Diagrams
4.4.1 Work from the
intersections
outwards, P(A) means the whole circle