14. measures of central tendency and dispersion

what are the descriptive statistics

1. measures of central tendency (mean, median mode)

2. measures of dispersion (range, standard deviation)

what are descriptive statistics

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

what are measures of central tendency

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

what is the mean

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

• most sensitive of the measures of central tendency as it includes all the values in the data set within the calculation - means it is more representative of the data as a whole

• mean is easily distorted by extreme values

what is the median

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

• extreme scores dont affect it

• easy to calculate

• less sensitive than the mean as actual values of lower and higher numbers are ignored and extreme values may be important

what is the mode

the most frequently occurring value in a set of data, in some sets there may be two modes (bi-modal) or no mode if all are different

• very easy to calculate

• crude measure

• when there are several modes it is not useful

measures of dispersion

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

what is 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 (allows for the fact that raw scores are often rounded up/down when they are recorded within research)

• only takes into account the two most extreme values and may be unrepresentative of data set as a whole

• does not indicate whether numbers are closely grouped around the mean or spread out

what is standard deviation

a sophisticated measure of dispersion in a set of scores, it tells us by how much on average each score deviates from the mean

the larger the standard deviation, the greater the dispersion/spread within a set of data

• much more previse as includes all values within final calculation

• can be distorted by a single extreme value - extreme values may not be revealed