frequency distributions

FREQUENCY DISTRIBUTIONS
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The frequency distribution diagram displays the maximum and minimum points, median, range and standard deviation of the serum granulysin level in a group with the mild presentation. The diagram also includes displays the grouping of observations into hospitalized, outpatients and the control group of the sample (64 patients in total). The range (the difference between the maximum and the minimum observations) displays the diversity or spread of the data. While the range has limitations because of the occurrence of outliers, the problem is solved by having a control group. The range sets boundaries or thresholds, such as a critical high or low and therefore informs the researcher whether a specific or number of observations has broken the set thresholds, and is useful especially in small data sets. It also helps to eliminate errors that might occur during data entry by singling out outliers. The maximum and minimum points indicate the spread of the observations. The median finds the central value by removing outliers to give a more overall view of the entire dataset. It provides a typical situation of the expected observations. The standard deviation measures the variability of the data around the average, mean or expected observations (Driscoll, Lecky and Crsoby, 2000). It, therefore, measures dispersion, that is, the difference between the average observations/values and the actual values. Standard deviation analysis the quality of the mean, in that, it shows how close the calculated mean is a representative of the actual data.

The data could have been presented using boxplots, histograms, scatterplots, or bar charts. Boxplots show the distribution of data along a straight line based on the minimum, maximum and range. They indicate the symmetry or skewness of a dataset while identifying outliers. However, the mean and the mode of the data cannot be identified in a box plot. Histograms are useful in displaying large data sets, by showing numbers within intervals. However, they do not show actual values.
Reference
Driscoll P, Lecky F, Crosby M An introduction to everyday statistics—2 Emergency Medicine Journal 2000;17:274-281.