Central Tendency and Variability II

Central Tendency and Variability II
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A] Briefly discuss the concept of mode, mean, median. What is it? How is it calculated? When would we use each one?
Measures of central tendency
The measures of central tendency in the form of the mode, median and mean show the position of data distribution, with values lying between the lowest and highest extremes of the data set. As such, there are useful to describe the behavior of distribution by focusing on the center, and the mean is typically used together with the measures of variability. In other words, measures of central tendency also represent the typical value, where data values congregate around.
Mode
The mode is the most common number within a set, and one needs to find the frequency of each number, and the mode is the number that is most frequent (Norman & Streiner, 2008). Typically sorting the data from the smallest to the largest fora data set makes it easier to identify the mode. A data set may have one unique mode, two modes (bimodal) or even multiple modes (multimodal) set. It is the most typical value in a series, where the values is concentrated and is the highest point in a frequency distribution curve. Since it is an actual representation of a value in the data set, it is a good representative of the data, and it is not affected by the outliers compared to the mean.
Mean
The mean is the average is a set of numbers, and one has to aggregate all the data and then divide by the number of observations/ elements/ frequency in the data set (Norman & Streiner, 2008). The mean is calculated as Æ©X/ N with Æ©X being the sum of items and N the number of observations. The measure takes into account all the values, while it is does not depend on position of values on the data series. Nonetheless, the man has an upward bias, meaning that it may give misleading conclusions. On average the data values tend to cluster around the mean and the extent to which the values deviate from the mean show the effect of outliers on the data.
Median
The median is the central value in a data distribution, meaning that it divides the values equally, with each section containing the same number of items (Michelson & Schofield, 2002). In cases where the frequency is in an odd number the middle part, while in the even number it is the mean if the two middle values. As such, the values are arranged depending on the magnitude of values, whereby there are values above the median and those below median. In most cases, the cumulative frequencies are necessary to calculate the median especially for the large data sets. The median is a useful measure of central tendency since it can be calculated distributions,...