Data analysis: descriptive statistics

What are measures of central tendency?

the general term for any measures of the average value in a set of numbers

What are examples of measures of central tendency?

mean, median and mode

What are measures of dispersion?

the general term for any measure of the spread of variation in a set of scores

What are examples of measures of dispersion?

range and standard deviation

Define mean

the average value which is calculated by adding all of the scores in a data set and then dividing the total by the number of scores

What are the advantages of mean?

it uses all of the scores in a data set making it more representative

What are the disadvantages of mean?

it is easily distorted by extreme values. Having just 1 extreme anomaly can bring the mean higher/lower than the majority of values

Define median

the middle score when the data is put in order from smallest to largest

What are the advantages of median?

extreme scores do not affect the median and it is relatively easy to calculate

What are the disadvantages of median?

not all scores are included in the final calculation

Define mode

the score that occurs the most often in a data set, there can be two (bi-modal) or even more

What are the advantages of mode?

very easy to calculate, good for analysing data in categories

What are the disadvantages of mode?

doesn’t really represent the whole data set, there may be 7 scores of ‘10’ but 6 scores of ‘1’ which becomes ignored

Define range

a simple measure of the spread of data. The lowest score is subtracted from the highest score and then we add 1 (to account for margins of error)

What are the advantages of range?

easy to calculate

What are the disadvantages of range?

it inly takes into account the most extreme values, doesn’t represent the whole data set

Define standard deviation

a sophisticated measure of the spread in a set of data. It tells us how much scores deviate from the mean

What are the advantages of standard deviation?

it is a much more precise measure of dispersion than the range as it includes all values within the calculation

What are the disadvantages of standard deviation?

it is easily distorted by extreme values

What does a low standard deviation suggest?

that the scores are closer to the mean - more dispersed - less valid as it is more likely to contain anomalies

What does a high standard deviation suggest?

that the scores are closer to the mean - less dispersed - more valid as it is less likely to contain anomalies