How do you find mode if mean and median is given?

Answer 1

With extreme difficulty, that is, you cannot.

The mode depends entirely upon the data items and the same mode can be found for different pairs of means and medians; similarly for any given pair of mean and median, there are many modes possible.

example:

The data sets {1, 1, 3, 4, 5, 6, 7, 8, 10}:

• mean: (1 + 1 + 3 + 4 + 5 + 6 + 7 + 8 + 19) ÷ 9 = 6
• median: [1, 1, 3, 4] , 5, [6, 7, 8, 19] = 5
• mode: [1, 1], 3, 4, 5, 6, 7, 8, 19 = 1

and {1, 2, 3, 4, 5, 6, 7, 7, 19}:

• mean: (1 + 2 + 3 + 4 + 5 + 6 + 7 + 7 + 19) ÷ 9 = 6
• median: [1, 2, 3, 4], 5, [6, 7, 7, 19] = 5
• mode: 1, 2, 3, 4, 5, 6, [7, 7], 19 = 7

both have mean 6 and median 5, but the first has a mode of 1 and the second a mode of 7 - you cannot tell the mode from the mean and median.