# Descriptive Statistics Research Papers

Where there are too many characteristics to be described in text, or several sub-groups of participants are being compared, tabular presentation becomes more convenient.

An example summarising the distribution of 11 categorical variables and 2 quantitative variables in the 2 phases of a before–after evaluation of the introduction of a care pathway for hip fracture  is presented in Table 1.

Figure 1b suggests that the value with highest frequency might be a useful descriptor of the centre of a distribution.

In practice, this can prove awkward: depending on the precision of measurement there may be no value occurring more than once.

Presentation of the mean and SD invites the reader to calculate the normal range and think of it as covering most of the distribution of values.

Another reason for presenting the SD is that it is required in calculations of sample size for approximately normally distributed outcomes, and can be used by readers in planning future studies.

A graphical display of approximately normally distributed real data (age at admission amongst 373 study participants) is shown in Figure 1c: with relatively small sample size a smooth distribution such as that shown in Figure 1a cannot be achieved. (c) Dotplot (each dot representing one value) of an approximate symmetrical distribution indicating the normal range: age in years at admission (When a distribution is skewed (Figure 1b) just one or two extreme values, ‘outliers’, in one of the tails of the distribution (to the right in Figure 1b) pull the mean away from the obvious central value.

The mean (82.9) and SD (6.8) of the age distribution lead to the normal range 69.3–96.5 years, which can be seen in Figure 1c to cover most of the ages in the sample: 14 subjects fall below 69.3 and 7 fall above 96.5, so that the range actually covers 352 (94.4%) of the 373 participants, close to the anticipated 95%. (c) Dotplot (each dot representing one value) of an approximate symmetrical distribution indicating the normal range: age in years at admission (Idealised and real data distributions. An alternative statistic describing central location is the median, defined as the point with 50% of the sample falling above it and 50% below.

Figure 1a shows an idealised symmetric distribution for a quantitative variable.

The mean might be used here to describe where the centre of the distribution lies and the SD to give an idea of how spread out values are around the centre.

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