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Write merits and demerits for various measures of central tendency.
The different measures of central tendency include: * Mean * Median * Mode
Mean is the sum of sampled values in a set of data divided by the number of items in the data. It is also known as the average.
Its merits include: * It is rigidly defined by its formula * It is easy to calculate and simple to understand * It represents all of the given data * It can be treated mathematically so it is widely used in statistical analysis. * It can be computed even if all of the details of the distributions are not known but some of the data and number of the data are known. * It is affected least by the fluctuation of sampling

Its demerits include: * It cannot be determined by inspection or the use of graphical location. * It is not suitable for qualitative data e.g. data concerning honesty or shopping habits * It is easily affected by extreme observations * It cannot be computed in the case where class intervals are open ended

Median is the number which appears in the middle in a given set of data. It divides the group of data into two equal parts.

Its merits include: * It is simple to use, one may just glance at data if arranged systematically and get the median * It is unaffected by extreme values * It has a specific value in a set of data * It can be estimated through a graphic presentation of data * It can be estimated even in an incomplete series of data * It has a real value and it is a better representative in a given data compared to the mean

its demerits include:- * It lacks representation because it is not based on all the items in a given set of data * It is unrealistic because if it falls between two middle values then it remains an approximate measure * the median is not capable if further algebraic treatment unlike the mean

Mode is the value that occurs most frequently in a given set of data.

Its merits include: * it is simple since a glance at a given set of data is enough to locate the modal value * it is less affected by marginal values in a series * it can be located graphically by use of a histogram * it is the best representative value in a given set of data * Mode calculation does not require knowledge of all items and frequencies in a given set of data

Its demerits include:

- It is an uncertain measure of central tendency * It is not capable of further algebraic treatment unlike the mean * Mode calculation involves grouping data and if the extent of grouping changes then the modal value will also change * When frequencies of items in a given set of data are identical then it becomes difficult to find the modal value * It does not represent all the items in a given set of data as it ignores extreme marginal frequencies

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