Mode Practice Questions

Mode is a measure of central tendency that represents the value that occurs most frequently in a dataset.

Example 1: Find the mode in the given set of data: 3, 6, 7, 15, 21, 23, 40, 23, 41, 23, 14, 12, 60, 23, 28.
Solution:

First arrange the given set of data in ascending order: 
3, 6, 7, 12, 14, 15, 21, 23, 23, 23, 23, 28, 40, 41, 60

Therefore, the mode of the data set is 23 since it has appeared in the set four times.

Example 2: Find the mode in the given set of data: 1, 3, 3, 3, 6, 6, 6, 4, 4, 10.
Solution:

First arrange the given set of data in ascending order: 
1, 3, 3, 3, 4, 4, 6, 6, 6, 10

Therefore, the mode of the data set is 3 and 6, because both 3 and 6 is repeated three times in the given set.

Example 3: For a class of 40 students marks obtained by them in math out of 50 are given below in the table. Find the mode of data given.

Solution:

Maximum Class Frequency = 23 
Class Interval corresponding to maximum frequency = 30-40
Modal class is 30-40

Lower limit of the modal class (l) = 30
Size of the class interval (h) = 10
Frequency of the modal class (f₁) = 23
Frequency of the class preceding the modal class (f₀) = 7
Frequency of the class succeeding the modal class (f₂)= 10

Using these values in the formula 
Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)]×h
⇒ Mode = 30 + [(23-7) / (2×23 - 7- 10)]×10
⇒ Mode = 35.51

Thus, mode of the dataset is 35.51

Practice Questions

Question 1 : Find the mode of the following dataset: 5, 8, 12, 8, 15, 8, 20, 12, 8, 25, 12, 8

Question 2 : A coffee shop records the number of cups of coffee sold per hour over a day: 15, 22, 18, 22, 20, 22, 19, 18, 22, 15, 20, 22, 18, 22, 20, 22. Find the mode and identify what type of mode this dataset represents (unimodal, bimodal, trimodal, or multimodal).

Question 3 : Calculate the mode for the following frequency distribution:

Question 4 : A dataset has a mean of 50 and a median of 48. Using the relationship Mode = 3 Median – 2 Mean, calculate the mode of this dataset.