statistics

Population

All the individual items that could be studied

Sample

A selection of items from the population

Subjects/sample

Individual items in a sample

Observations

Data collected from the subjects/sample

Variables

The differences between subjects you may want to study

Data

Numerical information used to interpret and extract meaning from

Quantitative

Information that possesses a directly measurable (numerical) value

Qualitative data

Information/data that in non-numerical in nature. Usually in the form of a descriptive. Sometimes converted to quantitative data for analysis

Categorical data

Qualitative data which fits into named categories with no in between categories (like blood group)

Nominal data

Qualitative data with no ordering to the categories (e.g. species of snail)

Ordinal data

Qualitative data which has ordering to the data (e.g. sporting scores, chilli hotness score) - ordering not mathematically linked

Discrete data

Quantitative data that can only take certain values (no half people in a room)

Continuous data

Qualitative data which can take any value within a given range

Distribution

Way of describing the way a dataset looks

3 ways of measuring central tendency

• mean

• Median

• Mode

Mean

Sum of all the values divided by the total number of values

What is mean represented by (population mean)

Mu (Greek letter)

What is mean represented by (sample from larger pop)

X bar

When is the median used

When the data is skewed - mean not reliable

Median

The point at which half of the data points are above and half are below

What happen to the median if there are an even number of values in the sample

The median is the mean of the two middle values

Resistant

Median is not affected by extreme values

Mode

Most frequently occurring event

When is the mode most useful

Nominal variables (e.g. eye color) where mean and median are not useful

Name of 2 modes

Bimodal

Name for more that 2 modes

Multimodal

Why isnt central tendancy enough

• 2 data sets may have the same means but completely different dispersion

Range

Max-min

How is variance represented

S²

what limits the usefullness of the range

strongly affected by outliers

what is the IQR

Q1-Q3

what does the cental box of a boxplot represent

IQR

what does the line in the box of the boxplot represent

median

what to the whiskers of a boxplot represent

the maximum and minimum

how is an observation determined to be an outlier

if it is more than 1.5 x IQR above the 3rd quartile or below the 1st quartile

variance definition

measurement of how far each number in a data set is from the mean and from every other number in the set

• overall degree that data points differ from the mean

what can the variance tell us

the spread/dispersion

steps to calculate variance

1. find difference between each value and the mean

2. square the differences

3. add the differences together

4. divide by the number of data points minus 1 (if working with a sample - if working with the population, divide by number of data points)

why do we quare the deviations when calculating variance

to account for negative numbers

what is the most commonly used measure of spread

standard deviation

when is standard deviation useful

as a measure of dispersion of NORMALLY DISTRIBUTED data

what is the 68-95-99.7 rule

no matter what the standard deviation and the mean are, the area between them is about 68%, the area between the mean ± 2S.D is 95%, the area between the mean ±3S.D is 99.7 percent

nearly all values/observations fall ..?

within 2 standard deviations of the mean

what can you use S.D for

to determine if your data are normally distributed

how to use S.D to determine if data are normally distributed

if the value of 2S.D ± mean is clearly impossible the data are NOT normally distributed. only if sample size is 50+

symbol for standard deviation

sigma

symbol for population variance

sigma squared

symbol for sample variance

s squared

symbol for population mean

mu

symbol for sample mean

x bar

description of normal distribution

• bell curve

• centered on mean

• most of data clustered around center

• in perfect normal distribution, mean, median and mode would be the same

kurtosis definition

measure of how wide or narrow the tails of distribution are

mesokurtic

• medium tailed

• medium outlier freq

• moderate kurtosis

• normal distribution

platykurtic

• thin tailed

• low outlier freq

• low kurtosis

• uniform distribution

leptokurtic

• fat tailed

• high outlier freq

• high kurtosis

• laplace distrubution

z score definition

• the number of standard deviation units than an observation is away from the population mean

positive vs negative z score

• if an observation has a value above pop. mean = +1sd = z score of 1

• if its -1sd = z score of -1

formula for z score

deviation from the mean divided by the standard deviation

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