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Example – 5. Calculate the mode of the following frequency distribution :

Solution :- To calculate mode we first prepare cumulative frequency table like this :

Here, L = 20, f_m = 26, f₁ = 11, f₂ = 14, i = 10. Using formula,
                        Mode = L + (f_m – f₁) / (2f_m – f₁ – f₂) × i
                                  = 20 + (26 – 11) / (2x26 – 11 – 14)×10
                                  = 20 + (15/27) × 10
                                  = 20 + 150/27 = 20 + 5.56 = 25.56

Mode by histogram :- First of all we draw histogram. Then we join the top right angular point of the rectangle with maximum frequency to the top right angular point of the just preceding rectangle and then the top left angular point of the rectangle with maximum frequency to the top left angular point of the just succeeding rectangle by straight line. From the point of intersection of these two lines a perpendicular is drawn on x-axis. The foot of perpendicular on the x-axis is the required mode.

Example – 6. For the following frequency distribution draw a histogram and then calculate the mode.

Solution :-

      fig. – 8 .

From the histogram, mode = 12.5 or 12.6.