The measure of central tendency is a single value that represents the whole set of observations. Given below is 5 measures of central tendency and their suitable application in real-life.
1) Mean - It is the average of all the observations. It is applicable to continuous data following normal distribution, i.e. the outliers or extreme values in the data set do not affect the average significantly.
Eg: Average score of a class of students, average height of a group of members.
2) Median - It is the middle most observation in the data set when it is arranged in ascending order. That is, the measure is based on position. It is applicable to continuous and discrete data not following normal distibution. That is, when there are outliers that can affect the centralization, the median is observed. It can be mostly related to revenue.
Eg: Average income of a group of associates, Average turnover of a company.
3) Mode - It is the value that occurs most number of times in the data set. It is applicable to discrete or continuous data concerning frequency or common occurance. In some cases, the data set may have two modes or no mode.
Eg: Movie with average popularity (measured from the number of tickets sold), average earthquake measurement in an area,
4) Geometric mean - It is the nth root of the product of n values. The geometric mean of two numbers, 6 and 8 is the square root of (6x8 = 48). It is used in the case of observations related to time.
Eg: Average rate of return in investment in a year is calculated by taking the root of the product of each year's rate of return.
5) Harmonic mean: It is the reciprocal of the arithmetic mean obtained from taking the values in reciprocal form. It is used when the values of a variable depend on other factors or determinants. That is, this measure is used to harmonize the values and then find their mean.
Eg:
a) Calculating the average speed on a car in a distance of 40 kms. from four different readings as:
100 km/hr in the first 10 kms
90 km/hr in the second 10 kms
110 km/hr in the third 10 kms
105 km/hr in the final 10 kms
b) Calculating the average score of a student based on the scores in written test and interview. This helps to eliminate two types of students
i) who score well in written test but score poorly in interview
ii) who score poorly in written test but score well in interview.
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