Measures of central tendency and dispersion

define Measures of central tendency:

Any measure which calculates an average value within a set of data

What are the ways that the ways that the average can be calculated?

• mean

• median

• mode

What is the mean?

Arithmetic average (add together, then divide by amount of numbers)

When can you use the mean?

• ratio data

• interval level data

Median:

If you line the data in order from smallest, to biggest – the middle value is the median

When can you use the median?

• ratio data

• interval data

• ordinal data

What is the mode?

The most common value/item in a data set

What are measures of dispersion:

A descriptive statistic that provides information about a 'typical' value for a data set

what can due used to show measures of dispersion?

• range

• Standard deviation

What is the range?

The difference b/w the highest and lowest data items in a data set

what is standard deviation?

• Shows the amount of variation in a data set.

• Assesses the spread of data around the mean

What are the strengths of using mean?

• Makes use of all values

• Good for interval data

what are the weaknesses of using the mean?

• Makes use of all values

• Good for interval data

What are the strengths of using the median?

• Not affected by extreme scores

• Good for ordinal data

What are the weaknesses of the median?

• Not as 'sensitive' as the mean because it doesn't sue all data

• Not used in many statistical tests

what are the strengths of the mode?

• unaffected by extreme values

• more useful for discrete data

• the only method that can be used when data is in categories (nominal data)

What are the weaknesses of the mode?

• not useful for describing data when there are multiple modes

• tells use nothing about other values in a distribution

What are the levels of measurement?

• nominal

• ordinal

• interval

• ratio

• (NOIR)

What is nominal data?

data are in separate categories (eg: grouping people by their fav football team)

What is ordinal data?

• data are ordered in some way (eg: put a list of fav football teams in order of liking)

• the difference b/w each item might not be the same (eg: dig difference in 1st and 2nd team, but not much b/w 2nd and 3rd)

What is interval data?

• measured using units of equal intervals (eg: counting correct answers or using any ‘public’ unit of measurement)

• many psychological studies are ‘plastic interval scales’ where the intervals are arbitrarily determined and so we can’t know for certain that there are equal intervals b/w the numbers

• but for the purposes of analysis, such data may be accepted as an interval

What is ratio data?

there is a true zero point as in most measures of physical quantities

What is a strength of using range?

Easy to calculate

What are the weaknesses of using range?

• Effected by extreme values

• Failed to take into account the distribution of numbers, eg: doesn't show whether most numbers are closely grouped around the mean or spread out evenly

Strengths of using standard deviation?

• Precise because it takes all data into account

• not difficult to calculate if you have a calculator

What is a weakness of Standard deviation?

It may hide some of the characteristics of the data set (eg: extreme values)

Overall - mean

not always representative of data as a whole and should always be considered alongside the SD

Overall - median

has strengths in that is can be used to describe a variety of data sets, including skewed data and non-nominal distributions

Overall - mode

only use mode when appropriate (eg: nominal data sets)

Overall - Range

useful for ordinal data or with highly skewed data or when making a quick calculation

Overall - SD

Best used together w/ the mean to describe interval data which is normally distributed