Measures of central tendency and dispersion

Question 1

Levels of measurement

Answer 1

• Nominal
• Ordinal
• Interval
• Ratio

Question 2

Nominal

Answer 2

Data is in separate categories, such as grouping people according to their favourite football team
e.g oxford united, manchester united

Question 3

Ordinal

Answer 3

Data is ordered in the same way e.g asking people to put a list of football teams in order of liking
- the difference between them is not the same and the individual may like the first item alot more than the second

Question 4

Interval

Answer 4

Data is measured using units of equal intervals such as when counting correct answers

Question 5

Ratio

Answer 5

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

Question 6

Measures of central tendency

Answer 6

Mean - adding up all data and dividing it by how many there are ( can only be used with ratio and interval data )
Median - middle value ordered in a list ( can be used with ratio, interval and ordinal data
Mode - value that is most common ( interval and ordinal data )

Question 7

Evaluation of the measures of central tendency

Answer 7

Mean - has the most sensitivity which means it can be distorted easily by one or a few extreme values and end up being misrepresentative
- cannot be used with nominal data

Median - not affected by extreme values so it can be useful
- appropriate for ordinal data
- easier to calculate
- not as sensitive as the mean

Mode - unaffected by extreme values
- useful for discrete data
- only method that can be used when data is in categories (nominal)
- not a useful way of describing data when there are several modes

Question 8

Measures of dispersion

Answer 8

Range - difference between the highest and lowest values and add a +1

standard deviation - measure of the average distance between each data item

Question 9

Evaluation of measures of dispersion

Answer 9

Range - easy to calculate
- affected by extreme values
- fails to take account of the distribution of the numbers e.g does not indicate if the numbers are closely grouped

Standard deviation - precise measure of dispersion because all the exact values are taken into account
- not difficult to calculate
- however can hide some of the characteristics of the data set e.g extreme values