measures of central tendency & dispersion

Question 1

name the measures of central tendency

Answer 1

• mean
• mode
• median

Question 2

name the measures of dispersion

Answer 2

• range
• standard deviation

Question 3

describe the mean
- include AO3

Answer 3

• average
• calculated by adding up all scores/values in data set & dividing by total number of scores there are

(+)
- most sensitive measure of central tendency as includes all scores/values in dataset = more representative of data as a whole

(-)
- easily distorted by extreme values

Question 4

describe the median
- include AO3

Answer 4

• middle value in data set when scores arranged lowest to highest

(+)
- extreme scores do not affect it
- easy to calculate

(-)
- less sensitive than the mean as actual values of lower/higher numbers are ignored & extreme values may be important

Question 5

describe the mode
- include AO3

Answer 5

• most frequently occurring score/value in data set
• in some data, there’s two modes (bi-modal) or no mode

(+)
- very easy to calculate
- for some data it is the only method you can use

(-)
- very crude measure as it can be very different from the mode/median & not representative of data set as a whole
- if there are several modes, it isn’t a useful piece of information

Question 6

describe the range
- include AO3

Answer 6

• simple calculation of spread of scores
• worked out by taking lowest value from highest value
  (and usually adding 1 = mathematical correction to allow for fact that raw scores often rounded up/down when recorded during research)

(+)
- easy to calculate

(-)
- only takes into account two most extreme values, which may be unrepresentative of whole data set
- influenced by outliers
- doesn’t indicate whether most numbers are closely grouped around mean or spread out

Question 7

describe the standard deviation
- include AO3

Answer 7

• much more sophisticated measure of dispersion
• single value which tells us how far scores deviate from mean
• larger the standard deviation = greater dispersion/spread within data set
  –> if taking about particular condition in experiment, it may indicate how not every participant was affected by IV in same way as data is widely spread, suggesting there may be few anomalous results
• low standard deviation = data tightly clustered around mean, which may imply that all participants responded in similar way

(+)
- much more precise measure of dispersion than range as it includes all values within final calculation

(-)
- can be distorted by single extreme value
- extreme values may not be revealed, unlike the range