measures of central tendency and dispersion Flashcards
what are the three three sections of measures of central tendency?
- mean
- median
- mode
what are descriptive statistics?
the use of graphs, tables and summary statistics to identify trends and analyse sets of data. They include measures of central tendency. These measures are ‘averages’ which give us information about the most typical values in a set of data.
what are measures of central tendency?
the general term for any measure of the average value in a set of data
explain what is meant by the mean
- what most of us will recognise as the average
- it is calculated by adding up all the scores or values in a data set and dividing this figure by the total number of scores there are
- it is the most sensitive measure of central tendency as it includes all of the scores/values in the data set within the calculation.
- this means it is more representative of the data as a whole
- however it is easily distorted by extreme values and therefore may have the capacity to make it unrepresentative.
explain what the median consists of
- is the middle value in a data set when scores are arranged from lowest to highest,
- In an odd number of scores, the median is easily identifiable
- In an even number of scores, the median is halfway between the two middle scores
- the strength of the median, unlike the mean, is that extreme scores do not effect it
- it is also easy to calculate
- however it is less sensitive than the mean as the actual value of lower and higher numbers are ignored and extreme values may not be important
explain what the mode is
- the mode is the most frequently occurring score/value within a data set.
- in some data sets there may be two modes- bi-modal or no mode at all if all the scores are different
- although the mode is very easy to calculate, it is a very crude measure
- it might be very different to the mean or median and therefore not representative of the whole data set
- when there are several modes in a data set it is not a very useful piece of information
- for some data- data in categories- the mode is the only method you can use e.g. if you asked your class to list their favourite dessert, the only way to identify the most ‘typical’ or average value would be to select the modal group
What are the different measures of dispersion?
- range
- standard deviation
what are measures of dispersion
- the general term for any measure of the spread or variation in a set of scores
- how far scores vary and differ from one another
explain what is meant by the range
- a simple calculation of the dispersion in a set of scores which is worked out by subtracting the LOWEST score from the HIGHEST score and adding 1 as a mathematical correction
- the 1 counts for the margin of error by those rounding up or down scores
evaluate the range
ADVANTAGES
- it is easy to calculate
DISADVANTAGES
- it only takes into account the two most extreme values, and this may be unrepresentative of the data set as a whole
- does not indicate whether most numbers are closely grouped around the mean or spread out- whereas the standard deviation does show this aspect of dispersion
explain what standard deviation is
- it is a much more sophisticated measure of dispersion in the standard deviation
- it is a single value that tells us how far scores deviate (move away) from the mean
- the larger the standard deviation is, the greater the dispersion or spread within a data set. If we are talking about a particular condition within an experiment, a larger standard deviation suggests that not all participants were effected by the IV in the same way because the data is quite widely spread. It may be that there are few anomalous results.
- a low standard deviation is a much more precise measure of dispersion than the range as it includes all values within the final calculation
- however for this reason, like the mean, it can be distorted by a single extreme value. Also, extreme values may not be revealed, unlike with the range
