Question 1. Find out the mode of the following marks obtained by 15 students in a class:
Marks : 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7.
Solution:
The mode is the most common number that occurs frequently in the given data.
Marks
4
5
6
7
8
9
10
Number of students
2
2
2
4
2
2
1
Here, we can see that 7 occurred most frequently.
Hence, Mode = 7
Question 2. Find out the mode from the following data :
125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125
Solution:
The frequency of given set of observations:
Values
125 175 225 325 375 Frequency
4
2
3
1
1
Here the maximum frequency is 4 which is 125.
Hence, Mode = 125
Question 3. Find the mode for the following series:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2
Solution:
Frequency of the given set of observations:
Values
7.2
7.3 7.4 7.5 7.6 7.7 Frequency 4
2
1
2
1
2
Here the maximum frequency is 4 which is 7.2.
Hence, mode = 7.2
Question 4. Find the mode of the following data in each case:
(i) 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
Solution:
First arrange the data in the ascending order:
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here we can clearly see that 14 occurs 4 times, hence it has the highest frequency.
So, mode = 14
(ii) 7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7
Solution:
Frequency of the given set of observations:
Values
7
9
12
13
15 18 25 Frequency
5
1
3
1
1
1
1
Here the maximum frequency is 5 which is 7.
Hence, mode = 7.
Question 5. The demand of different shirt size, as obtained by a survey, is given below:
Size: | 38 | 39 | 40 | 41 | 42 | 43 | 44 | Total |
Number of persons (wearing it) | 26 | 39 | 20 | 15 | 13 | 7 | 5 | 125 |
Find the modal shirt sizes, as observed from the survey.
Solution:
Frequency of the given set of observations:
Size:
38 39 40 41 42 43 44 Total Number of persons (wearing it) 26 39 20 15 13 7
5
125
Here the maximum frequency is 39 which is 39.
Hence, mode = 39.