Solved Examples on Mode of Grouped Data

Problem 1: Find the mode of grouped data presented in the table below:

Solution:

Modal class = 20 – 30

Lower limit of the modal class = (L) = 20

Frequency of the modal class = 15

Frequency of the preceding modal class = 8

Frequency of the next modal class = 12

Size of the class interval = (h) = 10.

⇒ Mode = 20 + 10{15-8/(2×15-8-12)}

⇒ Mode = 20 + 10{7/10]

⇒ Mode = 20 + 7 = 27

Therefore, Mode = 27

Problem 2: Given a set of numbers that is 1, 4, 2, 5, 6, 3, 7, 1, 10, 8, 9. Find the mean, median, and mode.

Solution:

Mean: 1+1+2+3+4+5+6+7+8+9+10 = 56

Thus, Mean = 56/10 = 5.6

Data in Ascending Order: 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

As there are 11 observations here, thus 6th observation is the middle most observation.

Thus, Median = 5

Mode = 1 {as it is repeated the highest number of times(2 times)}.

Problem 3: Calculate the mode for the following frequency distribution.

Solution:

Class 40-50 has the maximum frequency, so it is called the modal class.

l = 40, h = 10, f_k = 28, f_k-1 = 12, f_k+1 = 20

Mode = l + h{(f_k – f_k-1)/(2f_k – f_k-1 – f_k+1)}

Mode = 40 + 10{(28 – 12)/(2 × 28 – 12 – 20)}

Mode = 46.67

Hence, mode = 46.67

Problem 4: For a given distribution the values of mean and median are 45 and 43 respectively. Find the value of mode.

Solution:

We know,

Mode = 3 Median – 2 Mean

⇒ Mode = 3×43 – 2×45

⇒ Mode = 129 – 90 = 39

Mode of Grouped Data is used to identify the most frequently occurring frequency within the most frequent interval or class in a grouped frequency distribution. To find the mode of grouped data, we can utilize the mode formula discussed further in the article. For any grouped frequency distribution, the mode can be calculated with the help of the modal class, which represents the most frequent class in the dataset.

This article simplifies the concept of Mode of Grouped Data for readers of all levels, covering subtopics such as grouped data, its definition, the Mode of Grouped Data formula, and the empirical relation. We will also learn how to calculate the mode of grouped data using the formula.

In Statistics, the Mode or Modal Value in a data set is referred to as the value or number that occurs most frequently in the data set.