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The median of a set of data values is an important measure of the central tendency of the data. It gives us information about where the center of the given data lies. We now list some of the advantages and disadvantages of the median as a measure of the central tendency of the data.

1. Rigidly defined – It is rigidly defined. This means that there is a unique value of the median for a given set of data values. On the other hand, when calculating the mode it is possible to have two values for the mode (bimodal distributions).
2. Easy to understand – It is easily understood and easy to calculate. In some cases, it can be located merely by inspection.
3. Can be computed graphically – It is possible to compute the median graphically by drawing histograms.
4. Unaffected by extreme values – It is not at all affected by extreme values. This is because the median of the data is calculated on the basis of the relative positions of the data values. Since it is unaffected by the presence of extreme values it it used when studying skewed distributions.
5. Calculated for open-end classes – It can be calculated for distributions with open-end classes.
6. Used for qualitative data – We can use the median to study the central tendency for qualitative data where characteristics can be arranged in ascending or descending order. On the other hand, the arithmetic mean cannot be used when studying qualities such as beauty, intelligence, etc.
7. Minimizes total deviation – The total absolute deviations of the data values from the median is smaller than any other value. This means that the median is the best candidate for the central value of the data set.

1. Ambiguity for even observations – In the case of an even number of observations, the median cannot be determined exactly. We merely estimate it by taking the mean of two middle terms.
2. It is not based on all the observations. For example, the median of 10, 25, 50, 60, and 65 is 50. We can replace observations 10 and 25 with any two values which are smaller than 50 and observations 60 and 65 with any two values greater than 50 without affecting the value of the median. This property is sometimes described by saying that the median is insensitive.
3. It is not amenable to algebraic treatment. For example, given the mean of two data sets there is a formula for the combined arithmetic mean. On the other hand given the median of two data sets we cannot obtain the median of the combined data set.
4. Sampling fluctuations – As compared with the mean, it is affected much by fluctuations of sampling.
5. Tedious for large data sets – Medians require little arithmetic, so they are easy to find by hand for small sets of data. But arranging even a moderate number of observations in order is very tedious so finding the median by hand for larger sets of data is unpleasant.
6. The median can be calculated for grouped data sets only under the assumption that the data values are spread uniformly across any given interval.

### Uses/Applications of the Median:

1. Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude, e.g., to find the average intelligence among a group of people.
2. It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.
3. It helps us to identify if the distribution is symmetric or not. The mean and median of a symmetric distribution are close together. If the distribution is exactly symmetric, the mean and median are exactly the same. In a skewed distribution, the mean is farther out in the long tail than the median.

We summarize the key merits and demerits of the median in the table below: