Teaching Measures of Central Tendency Essay

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46).

The third measure of central tendency is the mode. Despite it being the last option of consideration by many analysts, it is a mostly utilized measure. The mode represents the most frequent observation in a data set. For example, if total scores of a football tournament in every match were tabulated as 2, 4, 6, 5, 2, 4, and 2, then the mode of these observations is 2 scores because this observation occurs thrice in the distribution.

The median contributes to the fourth measure of central tendency and it represents the value in the distribution that lies in the middle of the observations of interest. To obtain the median, arranging the observations in ascending order establishes the observation that lies in the middle of the arranged data. For example, in the above given observations of football scores, they can arranged in ascending order as 2, 2, 2, 4, 4, 5, 6, then looking at this order, 4 is the median of the observation as it lies mid the arrangement. In the event there happens to be an even distribution, then the median is the average of the two observations lying in the middle of the ascending arrangement (Donnelly, 2004, p. 44).

The fifth and the final measure in this paper are the distribution shapes and these will give a visual representation of central point of a distribution. The distribution shapes includes, normal or symmetrical distributions, skewed distributions constituting positively skewed distribution and negatively skewed distributions, bimodal distribution and uniform distributions.

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The symmetrical distribution takes the shape of a bell curve when one plots the observations and the mean lies in the center of the bell curve splitting the tails evenly. In addition, the mode is equivalent to the mean of the distribution. The skewed distributions usually involve a data set that has extreme outliers resulting to asymmetrical bell curve and the observation will tend to concentrate at either of the tail ends showing a lopsided distributions. These skewed distributions have the positively skewed distributions where the greatest amount of observations lies on the left side of the plotted distribution while negatively skewed distribution has most of its outliers concentrated in the far right. On its part, bimodal distribution will represent a two-humped distribution while a uniform distribution remains a rare observation because in nature it is difficult to observe same frequencies for different responses (Pathways courses, 2003).

In conclusion, the measures of central tendency give information of the distribution of observations that represents the data effectively and are important measures in analysis. Apart from the commonly used mean, mode, median, weighted mean and distribution shapes gives a different option to obtain information concerning distribution of any data set. However, despite all these methods giving this important information, many analysts prefer the mean or average that the mode. Nevertheless, they are all measures of central tendency and help to obtain information of the central distribution.....

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