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The mode is one of the measures of central tendency that can be calculated for a given set of data values (the others being the mean and the median). The mode or the modal value is by definition the value in a series of observations that occurs with the highest frequency. We now list some of the most important properties of the mode, its applications, and its merits and demerits as a measure of central tendency.

### Properties of Mode:

1. The mode is not unduly affected by extreme value, that is, values that are extremely high or extremely low. For example if we are given the following set of observations: 1, 1, 1, 1, 1, 2, 2, 100 The mean of the above set of data values is 13.625 which is clearly not representative of the above data values. However, the mode which is equal to 1 is clearly representative of a typical value from the above data set. This is one advantage of the mode compared to the mean.
2. The mode is not calculated on all observations in a data set.
3. The value of the mode can be computed graphically whereas the value of the mean cannot be calculated graphically.
4. The value of the mode can be calculated in open end distributions without knowing the class limits.
5. The mode can be conveniently found even if the frequency distribution has class intervals of unequal magnitude provided that the modal class and the classes succeeding and preceeding it are of the same magnitude.
6. Sometimes it may not be possible to calculate the mode. This happens if the data has a bimodal distribution in which there are two possible values for the mode.
7. We have the following relationship between the mean, median and the mode: \text{Mode = 3*Median - 2*Mean}

### Uses of Mode:

1. The mode can be used to describe qualitative phenomena. For example, if we want to compare consumer preferences for different types of products such as soap, shampoo, etc. we should find the modal preferences expressed by different groups of people.
2. It is the best measure of central tendency for highly skewed or non-normal distributions because it gives the point of maximum concentration of the data.
3. It is used when performing non-parametric tests in inferential statistics.

1. Mode is easy to calculate and understand. In some cases it can be located merely by inspection. It can also be estimated graphically from a histogram.
2. Mode is not at all affected by extreme observations and as such is preferred to arithmetic mean while dealing with extreme observations.
3. It can also be obtained in the case of open end classes in a frequency distribution. On the other hand the mean cannot be calculated if the frequency distribution has open ended class intervals.

1. Mode is not rigidly defined. It is ill-defined if the maximum frequency is repeated or if the maximum frequency occurs either, in the very beginning or at the end of the distribution or if the distribution is irregular.
2. Since mode is the value of X corresponding to the maximum frequency, it is not based on all the observations of the series. Even in the case of the continuous frequency distribution, mode depends on the frequencies of modal class and the classes preceding and succeeding it.
3. Mode is not suitable for further mathematical treatment. For example, from the modal values and the sizes of two or more series, we cannot find the mode of the combined series.
4. As compared with mean, mode is affected to a greater extent by the fluctuations of sampling.

Summary
Article Name
Properties of Mode - Uses and Advantages
Description
The mode is not calculated on all observations in a data set. The value of the mode can be computed graphically whereas the value of the mean cannot be calculated graphically. The value of the mode can be calculated in open end distributions without knowing the class limits. The mode can be conveniently found even if the frequency distribution has class intervals of unequal magnitude provided that the modal class and the classes succeeding and preceeding it are of the same magnitude.
Publisher Name
allthingsstatistics.com

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