Answer

Kurtosis

It is universally acknowledged in research that satisfactory knowledge of” measures of central tendency, dispersion and skewness” is insufficient for understanding distribution of data. Consequently, in addition to the aforestated variables, it is necessary to deploy a different measure to gain a clearer understanding of the outline of the distribution. This measure is known as Kurtosis. This measure, popularly ascribed to Prof. Karl Pearson has on various occasions been referred to as “Convexity of a Curve” (Rashinkar, 2020). Essentially, Kurtosis adds statistical logic by giving a measure of the extent of flatness of a distribution.

A study by Rashinkar (2020) defines Kurtosis as the extent of “flatness or peakedness” around the modal value of the frequency distribution. In situations where most scores are around the region of the central tendency values, the frequency distribution will be comparatively constricted in width. The extent of Kurtosis is determined with respect to “the peakedness” of a normal distribution graph.

Stages/ Categories of Kurtosis

Three categories of Kurtosis can be defined from extant literature: Mesokurtic, Leptokurtic, and platykurtic (Walker & Maddan, 2019).

Mesokurtic Distribution

This also referred to as the Normal Distribution and is regarded in scholarly circles as “standard”. Inferentially, this distribution is characterized by peaks which are congruent with those from normal curves. In other words, data that conforms to mesokurtic variety tend to have “excess kurtosis of zero or close to zero” (Rashinkar, 2020).

Applying this distribution to a hypothetical situation in criminal justice, a scenario in which the numbers of prisoners who are on parole are to be determined before they return for other crimes, or some technicalities. Arguing from the supposition that the prisoners began their terms at the same time, then Kurtosis can be applied to determine the rate of return (and rate of repeat offenses) to prison (Cunneen & Tauri, 2019).

Leptokurtic Distribution

            These are frequency distributions whose curves peak above the mesokurtic (normal) curve. As a result, they are comparatively higher than the other two and narrower as well, indicating a concentration of data around measures of central tendency. In statistical analysis, Leptokurtic phenomena point toward a “positive excess kurtosis” (Rashinkar, 2020). They indicate dense tails on both sides of the distribution, an attribution to the presence of a large number of outliers. In criminology, leptokurtic curves may be used to model the number of complaints against the police from members of the public (Cunneen & Tauri, 2019). Specifically, it could indicate an unusually high number of complaints in a specified month or week as the researcher may determine.

Platykurtic Distribution

This frequency distribution curve has a characteristically “flat topped” than the leptokurtic (normal curve) (Walker & Maddan, 2019). Thus, this curve is relatively lower than the normal distribution. In practical situations, platykurtic distributions generally point toward “negative excess kurtosis” (Rashinkar, 2020). The kurtosis reveals a distribution with flat tails. It could be used to model situations in criminology. For instance, it could help to show an unusually low number of complaints against the police by members of the public for specific months or weeks as may be the case.

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