Descriptive Statistics

Question 1

What is nominal data?

Give an example

Answer 1

Each item can only appear in one category. There is no order.

Example: asking people to name their favourite colour, shape or subject at

Question 2

What is ordinal data?

Give an example

Answer 2

Data is collected on a numerical, ordered scale but intervals are variable. So, a score of 8 is not twice as much as a score of 4.

May lack precision because it is based on subjective opinion rather than objective measure.

Example: rating how happy you are on a scale of 1-10 or 1st , 2nd & 3rd placement in a race.

Question 3

What is interval data?

Give an example

Answer 3

Data that is based on numerical scales that include unites of equal and precisely defined size.

This includes counting observations of in an observational study (8 tallies is twice as much as 4 tallies) or use of ‘public’ unit of measurements.

Example: Time, temperature

Question 4

What are descriptive statistics?

Answer 4

Provides a summary of a set of data drawn from a sample. This can then be applied to a whole target population (generalised).

Question 5

What do descriptive statistics include?

Answer 5

Descriptive statistics include measures of central tendency and measures of dispersion.

Question 6

What are measures of central tendency?

Answer 6

Measures of central tendency are ‘averages’ which gives us information about the most typical values in a set of data.


Question 7

What are the types of central tendency?

What type of data do they use?

Answer 7

Mean – Interval data only

Median – ordinal or interval data only

Mode – most useful for nominal data

Question 8

What does the mean measure?

Answer 8

Arithmetic average, add up all the scores and divide by the number of scores.

Question 9

What does the median measure?

Answer 9

Middle value, place scores in ascending order and select middle value. If there are two values in the middle, the mean of these is calculated.

Question 10

What does the mode measure?

Answer 10

Most frequent or common value, used with categorical/nominal data

Question 11

Strength of mean

Answer 11

Sensitive measure – includes all the scores/value in the data set within the calculation. Represents data set better than median or mode.

Question 12

Strength of median

Answer 12

Less affect by extreme scores – the median is only focused on the middle value. In some cases, may be more representative of the data set as a whole.

Question 13

Strength of mode

Answer 13

Relevant to categorical data – when data is ‘discrete’ i.e., represented in categories. Sometimes the mode is the only appropriate measure.

Question 14

Limitation of mean

Answer 14

May be unrepresentative – one very large or small number makes it distorted.

The median or the mode tend not to be so easily distorted

Question 15

Limitation of median

Answer 15

Less sensitive than the mean – the actual value of lower and higher numbers are ignored. Extreme values may be important

Question 16

Limitation of mode

Answer 16

An overly simple measure – the mode may be at one extreme. It is not a useful way of describing data when there are many modes.

Question 17

What are measures of dispersion?

What does it include?

Answer 17

Provides measures of variability (spread) of scores.

Includes the range and standard deviation.

Question 18

How is the range calculated?

Answer 18

The range…

Calculated by subtracting the lowest value from the highest value in a set of data.

Question 19

What is standard deviation?

Answer 19

Standard deviation – the spread of data around the mean

Question 20

What does a higher standard of deviation suggest?

Answer 20

A higher standard deviation (widespread) suggests not all participants were affected by the IV in the same way, the results are less reliable and there may be anomalous results.

Question 21

What does a lower standard of deviation suggest?

Answer 21

A lower standard deviation (narrow spread) means participants were affected in a similar way and the results are more reliable.

Question 22

What does the range measure?

Answer 22

the difference between highest to lowest value (sometimes 1 is added if values have been rounded up or down).

Question 23

What does standard deviation measure?

Answer 23

Measure of the average spread around the mean. The larger the standard deviation, the more spread out the data is.

Question 24

Strength of range?

Answer 24

Easy to calculate – arrange the values in order and subtract the smallest from largest.

Simple formula, easier than the standard deviation.

Question 25

Strength of standard deviation?

Answer 25

More precise than the range – includes all values within the calculation. More accurate picture of the overall distribution of data set.

Question 26

Limitation of range?

Answer 26

Does not account for the distribution of scores – the range does not indicate whether most numbers are closely grouped around the mean or spread out evenly. The standard deviation is a much better measure of dispersion in this respect.

Question 27

Limitation of standard deviation?

Answer 27

It may be misleading – can be distorted by extreme values. Also, extreme values may not be revealed, unlike with the range.