measures of central tendency

Measures of central tendency

• These inform us about the central or middle value for a set of data

• ways of calculating typical value for a set of data

Mean

• mean is calculated by adding up all the numbers and diving by the amount of numbers

• it makes use of the values of all data

• can be misrepresentative of data as a whole if there are extreme values

• it cannot be used with nominal data

Median

• middle value in an ordered list

• not affected by extreme scores

• not as ‘sensitive’ as the mean because not all values are reflected in the median

Mode

• most common value

• useful when the data is in categories e.g nominal

• not a useful way of describing data when there are several modes

Measures of dispersion

• set of data can also be described in terms of how dispersed or spread out the numbers are

• provides you with direct information

• easy to calculate

• affected by extreme scores

• doesn’t consider the number of observations in the data set

Standard deviation

• measure of spread data around the mean

• more precise measure of dispersion because all values considered

• difficult to calculate by hand

• may hide some of the characteristics of the data set e.g. extreme values

Normal distributions

• when measuring certain variables, the frequency of these measurements should form a bell-shaped curve

• bell shape is symmetrical

• most people are represented in the middle of the curve, with the mean, median and mode occupying the centre point

Skewed distribution

• they lean to one side or the other

Positively skew

• where most of the distribution is concentrated towards the left of the graph, with a long tail off to the right

• the mode remains at the highest point, while the median and the mean are dragged off to the right

Negative skew

• Data distribution has a longer tail on the left side of the number line

• mode and median are higher than the mean

Correlation

• illustrates the strength and direction of a relationship between two or more co-variables (things being measured)

• plotted on scattergrams

Positive correlation

Both co-variables increase or both decrease

Negative correlation

One increases while the other decreases

Zero correlation

No association

Difference between correlations and experiments

experiment:

• researcher controls the IV in order to measure the effect on the DV

• possible to establish a cause and effect

correlations:

• do not manipulate variables

• not possible to establish a case and effect