Unit 2 - Descriptive statistics

What are ‘descriptive statistics’?

Mathematical summaries of the data set. They can either focus on various forms of average, or on the spread of data. These summaries allow you to gain a brief insight into the overall results of a study and how likely it is that the data collected was reliable.

How many types of descriptive statistics are there?

Two - measures of central tendency and measures of dispersion.

What do ‘measures of central tendency’ provide?

An average score from within the data set or an indication of the middle of the data set. It includes mean, median and mode.

How is the ‘mean’ calculated?

By adding all the scores in the data set together and dividing the total number by the number of scores that were added.

What are some strengths and weaknesses of using the ‘mean’?

Strengths are that it is necessary for further statistical analysis such as standard deviation and it can be considered an accurate and sensitive measure of the average of a set of scores.

Weaknesses are that it is influenced by anomalous results and it may produce a ‘non-sense’ value not in the original data set.

How is the ‘median’ calculated?

By finding the mid-point in a set of data that has been placed in order. If the mid-point falls between two different scores, take the scores either side of the mid-point, add them together and divide the result by two.

What are some strengths and weaknesses of using the ‘median’?

Strengths are that it is not influenced by anomalous results and it can always be found when using ordinal or above data level.

Weaknesses are that it is not useful in further statistical analysis and may produce a ‘non-sense’ value that was not in the original data set.

How is the ‘mode’ calculated?

It does not require a calculation but is an identification of the most common score in a data set.

What are some strengths and weaknesses of using the ‘mode’?

A strength is that it can be used for data measured on a nominal scale.

A weakness is that there may be more than one result, or no results at all if the data set is quite varied.

What do ‘measures of dispersion’ provide?

An insight into how spread-out data is. The closer the scores are, the smaller the dispersion will be. Lower/smaller dispersions imply more reliable data with fewer anomalies. Measures of dispersion include range and standard deviation.

What is the ‘range’?

A value that shows the spread of data, representing the difference between the lowest and highest scores. It is calculated by taking away the lowest score from the highest score in the data set.

What are some strengths and weaknesses of using the ‘range’?

A strength of using the range is that the range is easy to calculate.

Weaknesses are that it is affected by anomalous numbers, and it fails to take account the distribution of numbers (whether they are closely grouped around the mean or spread out evenly).

What is ‘standard deviation’?

A value which represents the amount of variation of results from the mean score. It gives you an idea of how far the majority of the results are from the mean.

What percentage of results will be within one standard deviation?

68%, meaning they will be above or below the mean score denoted in standard deviation. The closer the scores are to the mean, the lower the standard deviation. This indicates a narrower distribution and fewer outliers, meaning results are consistent as 68% of the results will be very close to the mean score.

What are the strengths and weaknesses of using ‘standard deviation’?

Strengths of using standard deviation are that it is a precise measure of dispersion because all the exact values are taken into account, and it is not difficult to calculate with a calculator.

A weakness is that may ‘hide’ some characteristics of the data set (extreme/anomalous values).