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An introduction to everyday statistics—2
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1. P Driscoll,
2. F Lecky,
3. M Crosby
1. Accident and Emergency Department, Hope Hospital, Salford M6 8HD
1. Correspondence to: Mr Driscoll, Consultant in A&E Medicine (pdriscoll{at}hope.srht.nwest.nhs.uk)

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## Objectives

• Describe central tendency and variability

• Summarising datasets containing two variables

In covering these objectives we will deal with the following terms:

• Mean, median and mode

• Percentiles

• Interquartile range

• Standard deviation

• Standard error of the mean

In the first article of this series, we discussed graphical and tabular summaries of single datasets. This is a useful end point in its own right but often in clinical practice we also wish to compare datasets. Carrying this out by simply visually identifying the differences between two graphs or data columns lacks precision. Often therefore the central tendency and variability is also calculated so that more accurate comparisons can be made.

## Central tendency and variability

It is usually possible to add to the tabular or graphical summary, additional information showing where most of the values are and their spread. The former is known as the central tendency and the latter the variability of the distribution. Generally these summary statistics should not be given to more than one extra decimal place over the raw data.

Key point

Central tendency and variability are common methods of summarising ordinal and quantitative data

### CENTRAL TENDENCY

There are a variety of methods for describing where most of the data are collecting. The choice depends upon the type of data being analysed (table 1).

View this table:
Table 1

Applicability of measure of central tendency

#### Mean

This commonly used term refers to the sum of all the values divided by the number of data points. To demonstrate this consider the following example. Dr Egbert Everard received much praise for his study on paediatric admissions on one day to the A&E Department of Deathstar General (article 1). Suitably encouraged, he reviews the waiting time for the 48 paediatric cases involved in the study (table 2).

View this table:
Table 2

Waiting time for paediatric A&E admissions in one day to Deathstar General

Considering cases 1 to 12, the …

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