Descriptive statistics

What are measures of central tendency? AO1

• Describe a data set by identifying a central score that represents the general trend of data - typical/average score

• Eg mean, median & mode

Mean AO1

• Average value of all scores

• Calculated by adding together all of the scores in a data set & dividing the total by the number of scores

Mean strength AO3

• P - takes into account ALL of the scores

• E - some researchers argue that even the extreme values in a data set are important in “telling the whole story”

• T - the mean misses nothing out & gives a more valid measure than the median & mode

Mean limitation AO3

• P - most sensitive measure of central tendency

• E - can be skewed or distorted by outliers

• T - measure may be unreliable as misrepresents the true tendency of data set

Median AO1

• The middle value

• Calculated by arranging all scores from lowest to highest & crossing one off from each side until the middle is reached

Median strength AO3

• P - unaffected by outliers

• E - only interested in what occurs in the middle of a data set & not at the extremes

• T - more representable than the mean

Median limitation AO3

• P - less sensitive than the mean

• E - can be argued that it isn’t a true representation of ALL the scores as it doesn’t take into account the extreme scores

Mode AO1

• Most frequent value

• May be 2 modes (bimodal)

• Only measure of central tendency you can use when behaviours are in categories

Mode strength AO3

• P - will never be a decimal score

• E - some researchers don’t like averages that are decimals as they can be meaningless (eg someone can’t score 2.5 goals)

• T - unaffected by extreme scores so useful with large data sets

Mode limitation AO3

• P - relies on there being a score which occurs more than others

• E - may not always be the case or there might be two or more modes (bimodal)

• T - sometimes most frequent scores might be at one end of the data set so not helpful in measuring central tendency

What are measures of dispersion? AO1

Shows how spread out a spread of scores are

Range AO1

• Measures the spread of data

• Calculated by subtracting the lowest score from the highest score

Range strength AO3

• P - often used in conjunction with the median

• E - the median analyses what’s happening in the middle of data whereas the range analyses what’s happening at either end

• T - shows the spread of scores in a data set

Range limitation AO3

• P - distorted by outliers

• E - can also be misleading as based on highest & lowest values

• T - range may suggest that the scores are quite spread out when most of them were close to the mean

Standard deviation AO1

• Tells us how far scores deviate from the mean

• Larger standard deviation = larger the dispersion, more variety, curve will be long & flat

• Small standard deviation = smaller the dispersion, less variety, curve will be tall & thin

Standard deviation strength AO3

• P - takes into account all scores & uses the mean

• E - gives useful info that takes us beyond the mean eg mean might be the same for 2 groups but the s.d may be different 

Standard deviation limitation AO3

• P - can be impacted by a distorted mean

• E - if the mean has been skewed by outliers than the s.d will be misleading

• T - may not truly reflect the spread of scores in a data set