# Measures of Central Tendency

## Introduction

Measures of central tendency are values that fall in the midline of a given data set (Dodge, 2003). Measures of central tendency are often used in research to get an idea of where most data values lie. Other data measures that are closely related to measures of central tendency are variance and standard deviation. The most commonly used measures of central tendency are mean, mode and median. These measures are mostly used by primary researchers during data analysis. This paper will examine the use of mean in a chosen article.

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## Description of the measure of central tendency (Mean)

Mean is a measure of central tendency that denotes the numerical center of a data set (Wall, Boen & Tweedie, 2004). Mean can either be an arithmetic mean, a geometric mean, or a weighted mean. Arithmetic mean is used to analyze data values that can be added and divided by a particular number. The arithmetic mean is closely related to the average value of data.

However, when analyzing grouped data weighted mean is more appropriate. This is because in grouped data a researcher should put emphasis on a certain group of data. None of the two types of mean is more important than the other. They both have situations in which they are applicable. Mean is often used to measure interval and ratio of symmetrical data.

Mean as a measure of central tendency has a number of characteristics; for a given set of data, there is only one mean value, all the values in a set of data play a part in its calculation, it falls at the centre of a data set. However, mean is not a good measure for all sets of data. It is only used to analyze quantitative data. For instance, there is no mean for religious affiliation. In addition, mean is affected by extreme values. In such a case, mean does not reflect where the average figure lies. Mean is often used alongside other measures of central tendency and is never used alone when analyzing data.

## Brief description of the study in the article

The article under review is titled ‘Gingival Recession: Prevalence, Extension and severity in adults’ by Marini et al. The article was published in the Journal of Applied Oral Sciences in 2004. The study was conducted in Sao Paulo, Brazil. The sample size was 380 adults aged 20 years and above seeking treatment at Bauru dental school. To ensure that data obtained was accurate, only one dentist examined all the teeth and rated the degree of gingival recession. Recessions was classified into class one, class two, class three, and class four.

The data obtained showed that 89 percent of the subjects showed gingival recession on one tooth (Marini et al 2001). The overall pattern of gingival recession showed that class one gingival recession was the most common. The degree of gingival recession increased with age. Older patients tended to have class three and class four gingival recessions.

The results also showed a marked difference between the mandible and the maxilla. The mandibular teeth were affected by gingival recession more than the maxillary teeth (Marini et al 2001). A difference was also noted between the mandibular teeth. Mandibular incisors were most affected. The results indicated that the dentists and dental hygienists should put emphasis on the diagnosis and treatment of gingival recession. Because the results showed that gingival recession is more prevalent in elderly patients, the researchers recommended a thorough examination of the etiologic agents.

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## Description of how mean was used in the study

The measure of central tendency used in this article is mean. It is used in the analysis of data relating to the number of teeth affected and the number of sites on the gum in with recession. The total number of teeth showing gingival recession was obtained and then the sum of the values was divided by the number of patients examined per age group. The process was repeated for the oral sites showing recession.

## Explanation of how the measure is appropriate and how assumptions were met

Arithmetic mean was used in this study. Arithmetic mean is more suited for simple or ungrouped data. Therefore, for this study a weighted mean would have been more appropriate. However, it is important to note that the researchers were able to draw meaningful conclusions from the results. The purpose of the study plays a role in the selection of measures to use. In this study emphasis was laid on prevalence of gingival recession in adults seeking dental treatment. The research was not intended to focus on the age distribution of the condition. Therefore, it can be concluded that the measure of central tendency used is appropriate. This is because data in this study is quantitative.

Mean is generally assumed to be an average. In the study the average number of teeth and sites showing gingival recession were obtained. In so far as the objectives of the study are concerned, the values obtained were useful in drawing conclusions. However, the mean does not give any sign that there could have been extreme values. For instance, some subjects could have had more than ten teeth showing gingival recessions. The mean number of teeth showing gingival recession in the study is 3.7. The measure was obtained using the total number of patients examined. This overlooked the fact that some subjects may have been free from gingival recessions.

## Identification of levels of measurement of the variables and appropriateness of the levels of measurement

In this study ordinal level of measurement was used. The variables in the study were age and the degree of recession. Age groups in the study were: 20-29, 30-39, 40-49, and above fifty. Gingival recession was scored using a defined scale and the values obtained were then arranged into class one, class two, class three and class four gingival recession. This level of measurement of variables is appropriate for the study because the ordinal variables can be ranked or arranged in a certain order. In this case gingival recession is grouped into four classes. Class four is the highest level of recession while class one is the lowest level of gingival recession. The study sought to determine the severity of gingival recession in adults.

## How data was displayed and appropriateness of the display

The data was displayed using tables and bar graphs. The data on the prevalence and extent of recession was displayed on tables. Data on intraoral distribution of gingival recession was displayed using a bar graph. The severity of gingival recession according to age was displayed in a separate bar graph.

Use of a table to display prevalence and extension is appropriate. This is because two types of variables were displayed on the same table. This enables the reader to compare and contrast the data variables.

Use of a bar a graph to display intraoral distribution of gingival recession is also appropriate. This is because the bar graph enables the display of data according to the dental arrangement in the oral cavity. At a glance a reader is able to tell which groups of teeth were more affected than others. The bar graph used to display the severity of gingival recession according to age group is appropriate for this kind of data. The reader is able to deduce certain conclusions by looking at the graph. The reader is in a position to see which age group is affected and by which class of recession.

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## Conclusion

Measures of central tendency are measures used to represent a midline of a data set. The most commonly used measures of central tendency are mean, mode and median. Mean is a calculated value that lies at the center of a data set.

## Works Cited

Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford: OUP.

Marini et al. (2004). Gingival Recession: Prevalence, Extension and Severity in Adults.

J Appl Oral Sci., 12 (3), 21-29.

Wall, M., Boen, J. & Tweedie, R. (2001). An effective confidence interval for the mean with samples of size one and two. The American Statistician.

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