Week 8: descriptive statistics II

How do we measure the spread of a dataset?

How much the scores vary = dispersion

Range, IQ range, STDEV

What is the range

Largest data point - smallest data point

Tells us nothing about scores in between

Most rudimentary level of analysis

Outline the IQ range

Measures the spread of the middle 50% of scores

After splitting data into quarters, difference between the first and third quartiles (quarters)

Median = 2nd quartile

Q3-Q1

Outline standard deviation

The measure of variation around the mean- measures every data point against the mean

The higher the STDEV, the larger the spread of scores

Very robust, can compare STDEVs of different populations

Gives an indication of what is happening between the min and max of a dataset

How is STDEV calculated?

The square root of the variance (S²)

What do graphs do

Represent data visually

Indicate patterns within the data

Use them to decide how to analyse your data

Use them to illustrate findings

What are the types of graphs

1. bar (histograms)

2. stem and leaf plots

3. box plots

4. scatterplots

Which type of data is in bar graphs

ordinal or nominal

What is a bar graph

Frequency data

Direct relationship between the area covered by each bar and the frequency of an occurence

What is a stem and leaf plot

Stems are the first figure of the number (0, 1, 2)

Leaves are the rest of the number

Stems can have two digits

Stem: Leaves:

0 48

1 0345

2 7

04, 08, 10, 13, 14, 15, 27

Outline box and whisker diagrams / box plots

summarise the lower quartile and upper quartile (Q1 an Q3)

median

minimum

maximum

outliers

What is an outlier in a box and whisker plot?

A data point that is 1.5 x interquartile range above Q3 or below Q1

Using SD- 2-3 SDs from the mean

Outline scatterplots

Shows the relationship between variables

Each point on the plot = 1 set of data or person w/ two variables linked to them/it

If data does not look random, probs a relationship going on