Measures of central tendency and dispersion

What are measures of central tendency?

Descriptive statistics include measures of central tendency. These measures are ‘averages’ which give us information about the most typical values in a set of data. There are three of these to consider: the mean, the median and the mode.

What is measures of dispersion?

Measures of dispersion are based on the spread of scores. That is, how far scores vary and diff er from one another. We shall focus on two of these – the range and the standard deviation.

What is bimodal distribution?

In some data sets there may be two modes (bi-modal)

What are the strengths of using mean?

Strengths of mean=

most sensitive measure because it takes into account all of the data points and the distance between each of them

What is the limitation of mean?

Limitations of mean=

easily distorted by extreme values. Cannot be used meaningfully with nominal levels of measurement

What is the strenghts of using median?

Strengths of using median=

Not affected by outliers as differences between data points are not accounted for, only their rank position. Easier to determine than the mean

What are the limitaitons of using median?

Limitations of using median=

not as precised as a measure as the exact values are not reflected in the result

What are the strengths of using mode?

Strengths of using mode=

not affected by outliers. Onlymethods that can be meaninfully used on nominal levels of measurement

What are the limitaions of using mode?

Limitations of using mode=

not as useful when there are more than 2/several modes. Tells us nothing about the other values in the data set.

What are the strengths and limitaitons of using range?

Strengths and limitations of using range=

strengths=

• easy to use

limitations=

• strongly affected by outliers. does not indicare the distribution of data points within thuis range i.e whether theyre closely grouped around the mean or spread evenly or more dispersed

What is standard deviation (SD)?

SD is the average distance between each data point alone or below the mean, ignoring ± values. INterpreted using a normal distribution curve that tells us that 68% of a population will be within ± 1 SD of the mean, 95% within 2 SDs and 99.74% within 3SDs

What are the strength of using SD?

Strengths of using SD=

precise measure of dispersion as it takes all the exact values into account. Not difficult to calculate as longa s you have a calculator

What are the limitations of using SD?

Limitations of using SD=

May ride some of the characteristics of a data set e.g does tend to mask out lying values as it is an average of the distances

How to tell if the data is dispersed around the mean or not?

The rule is that the higher the SD, the more the data is dispersed around the mean; the lower it is, the more data points that are clustered closely to the mean.