Measures of Central Tendency by DR. BORNWELL SIKATEYO - UNZA SCHOOL OF MEDICINE - Biostatistics-unza

DR. BORNWELL SIKATEYO UNZA SCHOOL OF MEDICINE MEASURES OF CENTRAL TENDENCY Learning objectives At the end of this lecture, you should be able to: Appreciate the use and calculation of means, medians and modes which are measures of central tendency Measures of Central Tendency A measure of central tendency is a univariate statistic that indicates, in one manner or another, the average or typical observed value of a variable in a data set, or put otherwise, the center of the frequency distribution of the data. How to Calculate Averages We consider three measures of central tendency that are appropriate for three different levels of measurement (nominal, ordinal, and interval). These are the mean, median and mode. The measures of central tendency, can be calculated from three different “starting points”: a list of observed values (i.e., raw data, e.g., one column in a data spread sheet); a frequency table (or bar graph); a histogram and. The Mode The mode (or modal value) of a variable in a data set is the value of the variable that is observed most frequently in that data (or, given a continuous frequency curve, is at the point of greatest density). Note: the mode is the value that is observed most frequently, not the frequency itself. The mode is defined for every type of variable [i.e., nominal, ordinal, interval, or ratio]. However, the mode is used as a measure of central tendency primarily for nominal variables only. How To Calculate the Mode Given a list of observed values (raw data): Construct a frequency table (see next slide). How To Calculate the Mode (cont.) Given a frequency table or bar graph (or having constructed one): observe which value in the table (or graph) has the greatest (absolute or relative) frequency; the most frequent value (not the frequency itself) is the mode. How To Calculate the Mode (cont.) Notice that the modal number of problem sets turned in is 5, even though most students turned in fewer than 5, So if we recoded the variable to create just two dichotomous categories: (a) turned in all 5 (b) did not turn in all 5 the latter (i.e. did not turn in all 5) category becomes the modal category How To Calculate the Mode (continued) Given a continuous frequency curve: the mode is the value of the variable under the highest point of the frequency curve (the point with the greatest density of observed values). Advantages of the mode It is easy to understand and calculate. It is not affected by extreme large or small values. It can be useful for qualitative data. Can be located graphically. Disadvantages of the mode Its computation is not based on all values as is the case for the mean. It will not be well defined if the data consists of small number of values (it is possible that there can be more than one modal value). It is not capable of further mathematical treatment. Sometimes the data may not have a mode at all. The Median The median (or median value) of a variable in a data set is: the value in the middle of the observations, in the sense that no more than half of the cases have lower values and no more than half of the cases have higher values or, more generally, such that no more than half of the cases have values that lie on either side of the median value.