. Measures of Central Tendency Introduction: One of the most important objectives of Statistical analysis is to get one single value that describes the characteristic of the entire value for data. Such a value represent the measure of central tendency for the complete data. The word average is very commonly used in day-to-day conversation.
For example, we often talk of average boy in a class, average height or average life of Sir Ronald Fisher an Indian, average income, etc,. Sir Ronald Fisher who is known to be a father of statistics and he made his pioneering contributions in the applications of statistics in various disciplines. . .
Average - Recall There are several measures of central tendency for the data. They are • Arithmetic Mean • Median • Mode • Geometric Mean • Harmonic Mean Arithmetic Mean (discrete case) Arithmetic mean of a set of observations is their sum divided by the number of observations. The observation are classified into a) Ungrouped data and b) Grouped data. a) Ungrouped data (i) Direct Method: ...
/ where X is Arithmetic Mean, ∑ X is sum of all the values of the variable X and n is number of observations. - - Descriptive statistics and probability (ii) Short-cut method The arithmetic mean can be calculated by using any arbitrary value A as origin and write d as the deviation of the variable X then, X = A + n / where d = X – A . b) Grouped data (i) Direct method The formula for computing the mean is X = N fx where f is frequency, X is the variable, N = ∑ f i.e. total frequency.
(ii) Short-cut method The arithmetic mean is computed by applying the following formula: X = A + N fd , where A is assumed mean, d = X – A, N = ∑f Arithmetic mean for Continuous case The arithmetic mean may be computed by applying any of the following methods: (i) Direct method (ii) Short-cut method (iii) Step deviation method (i) Direct method When direct method is used arithmetic mean