Stats

Measure of central tendency

A value which describes the centre of the data (mean, median, mode) - position in the data set

When to use each MMM

Mode - qualitative + quantitative

Media - quantitative + extremes

Mean - quantative + accuracte

How to find quartiles

n/4, n/2, 3n/4

If decimal, round up

If whole number, take an average with the next value above.

Interpolation equation + assumption

data is evenly distributed

X-small / Big-small

What does Variance measure

Average squared difference from the mean

What does standard deviation shown

Average distance from the mean

Coding formula

y = x-a/ b

meanY =meanx-a/b

SDy=SDx/b

Outliers and process name

A data point which significantly deviates from the other oberservations in the data set

Removing abnormal values is cleaning the data

Tests for outliers

Quartiles: UL = Q3+k(Q3-Q1), LL = Q1-k(Q3-Q1)

Mean and SD test: UL = Mean+kSD, LL= Mean-kSD

Histogram Formulae

Area = KF

If k =1

FD = F/CW

Bivariate Data

Pairs of values for 2 variables. Uses a scatter diagram.

Independent/ expanatory variable (changed) x axis

Dependent/ response variable (measure) y axis

Describe a regression line

A line which minimises the sum of the squares of the distances of each data point from the line.

Which direction to use a regression line

If you know the independent/ X, you can find the dependan/ Y.

This is line Y on X, to do the other way, you would need X on Y

Can only use it this way round. Can only use data within the set or its extrapolation

Experiment meaning

a repeatable process which gives rise to a number of outcomes

Event meaning

collection of one or more outcomes

Sample space

the set of all possible outcomes

Independent vs mutually exclusive events

Mutually exclusive= P(AUB) = PA+PB

Events have no outcomes in common

Independent = P(AnB) = PA x PB

One event has no effect on another

What is a random variable and what are its possible outcomes

Variable whose value depends on the result of a random event. The range of result values is the sample spece.

What is it called where all probabilities are the same

Discrete uniform distribution

When can binomial distribution be used

• Either success or fail (2 outcomes)

• fixed probability

• set number of trials

• trials are independent from eachother

population parameter

a value which sumarises the characteristics of the population (mean, variance etc.) It is what is tested in hypothesis testing

test statistic

A test statistic is a numerical value calculated from a sample of data during hypothesis testing. It is used to determine how far the sample statistic deviates from the null hypothesis

Notation for PMCC

r = the PMCC for the sample

p = the PMCC for the population

What does PMCC measure

The type and strength of linear correlation between 2 variables

Linear association of 2 variables