measures of central tendency and dispersion

Question 1

what is descriptive statistics?

Answer 1

the use of graphs, tables and summary statistics to identify trends and analyse sets of data

Question 2

what are measures of central tendency?

Answer 2

the general term for any measure of the average value in a set of data

Question 3

what is the mean?

Answer 3

the arithmetic average calculated by adding up all the values in a set of data and dividing by the number of values

Question 4

what is the median?

Answer 4

the central value in a set of data when values are arranged from highest to lowest

Question 5

what is the mode?

Answer 5

the most frequently occurring value in a set of data

Question 6

evaluation of mean

Answer 6

+ accurate
+ representative - includes all data
- influence by anomalous or outlying data, which may skew the mean and make the data less representative of the sample

Question 7

evaluation of median

Answer 7

+ not affected by extreme scores
- less representative of data set as it doesn’t take into account all data

Question 8

evaluation of mode

Answer 8

+ useful when we have categorical data that cannot be ordered or added / divided
- less sensitive and does not utilise all data

Question 9

what are measures of dispersion?

Answer 9

they are based on the spread of scores, focusing now how scores vary and differ from one another

Question 10

what is the range?

Answer 10

a simple calculation of the spread of scores that is worked out by taking the lowest value from the highest value and (usually) adding one

Question 11

why do you add 1 when you calculate the range?

Answer 11

• it is a mathematical correction that allows for the fact that raw scores are often rounded up (or down) when they are recorded within research
• eg. (17-5) + 1 = 13

Question 12

what is the standard deviation?

Answer 12

a sophisticated measure of dispersion which is a single value that tells us how far scores deviate from the mean

Question 13

what does a large standard deviation suggest?

Answer 13

• a greater dispersion or spread within a set of data
• in a particular condition within an experiment, it suggests that not all participants were affected by the IV in the same way because the data is quite widely spread
• it may be there are are a lot of anomalous results

Question 14

what does a low standard deviation suggest?

Answer 14

• it reflects the fact that all the data is tightly clustered around the mean
• this might imply that all participants responded in a fairly similar way

Question 15

evaluation of range

Answer 15

+ easy to calculate
+ identifies the existence of extreme values
- doesn’t show variation within the data, just the top and bottom
- will be skewed by extreme data

Question 16

evaluation of standard deviation

Answer 16

+ much more sensitive than the range
+ more representative of the data set as it uses all data
+ shows the variance within the data
- can be affected by anomalous or extreme values, which could indicate greater variance than actually exists in the majority of the data set

Question 17

for which type of data do you use each measure of central tendency or dispersion?

Answer 17

• mean: interval data
• median: ordinal data
• mode: nominal data
• range: ordinal data
• standard deviation: interval data