Geometric mean is defined only for non-zero positive values. Therefore in order to use geometric mean all the observations must be positive and greater than zero. Since geometric mean has the effect of reducing the influence of large items therefore it is used in the calculations of index numbers, average of ratios, and rates of change etc.
Geometric Mean of Ungrouped Data
If the data is not presented in the frequency distribution then the geometric mean can be calculated by simply taking the log of all observations, adding them up, dividing them by total number of observations and taking antilog of the resultant number. The calculation of geometric mean can be elaborated with the help of following problem.
Problem: A student got the following scores (out of 100) in different subjects in an examination: Urdu: 8, English: 67, Biology: 85, Chemistry: 35, Physics: 50, Math: 100. Find the geometric mean.
Geometric Mean of Grouped Data
If the data is presented in the frequency distribution then we have to first calculate the mid points of each class interval, take antilog of the mid points, multiply them with the corresponding frequencies, add the resulting values, divide them by sum of frequencies and take antilog of the final number. Geometric mean calculation of grouped data can be elaborated with the help of following problem.
Problem: Given a frequency distribution calculate the Geometric Mean.