Question : Find the mode for the given distribution (rounded off to two decimal places).
| Class Interval | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |
| Frequency | 8 | 7 | 6 | 9 | 11 | 10 |
Option 1: 35.25
Option 2: 40.25
Option 3: 30.33
Option 4: 28.33
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Correct Answer: 28.33
Solution :
Here, the maximum frequency is 11, and the corresponding class is 25–30.
So the modal class is 25–30.
Now lower limit of the modal class ($l$) = 25,
Frequency of the modal class ($f_1$) = 11
Frequency of the preceding modal class ($f_0$) = 9
Frequency of the succeeding modal class ($f_2$) = 10
class size ($h$) = 5
We know, mode = $l + (\frac{f_1-f_0}{2f_1-f_0-f_2})×h$
= $25 + (\frac{11-9}{2(11)-9-10})×5$
= $25 + (\frac{2}{3})×5$
= $25 + 3.33$
= $28.33$
Hence, the correct answer is 28.33.
Related Questions
Question : Refer to the following data table and answer the question.
| Division /Standard | Boys | Girls |
| A/5 | 20 | 30 |
| B/5 | 15 | 20 |
| C/5 | 30 | 10 |
| A/6 | 30 | 25 |
| B/6 | 30 | 25 |
| C/6 | 30 | 20 |
What is the ratio of number of the boys to girls?
Option 1: 26 : 31
Option 2: 31 : 26
Option 3: 33 : 28
Option 4: 28 : 33
Question : Calculate the mean from the following table.
| Scores | Frequencies |
| 0-10 | 2 |
| 10-20 | 4 |
| 20-30 | 12 |
| 30-40 | 21 |
| 40-50 | 6 |
| 50-60 | 3 |
| 60-70 | 2 |
Option 1: 34.2
Option 2: 33.4
Option 3: 32.6
Option 4: 35.8
Question : The table given below shows the number of salesmen in five companies.
| Companies | Salesman |
| C1 | 35 |
| C2 | 10 |
| C3 | 30 |
| C4 | 5 |
| C5 | 15 |
What is the average number of salesmen in C2, C4, and C5?
Option 1: 5
Option 2: 10
Option 3: 15
Option 4: 20
Question : The following table shows the marks distribution among the students in a class.
| Marks | No.of Students |
| Less than 10 | 2 |
| Less than 20 | 5 |
| Less than 30 | 6 |
| Less than 40 | 8 |
| Less than 50 | 10 |
How many students scored marks between 20 and 30?
Option 1: 2
Option 2: 5
Option 3: 1
Option 4: 6
Question : Refer to the data table and answer the following question.
| Marks | Number of students |
| 40 and above | 25 |
| 30 and above | 44 |
| 20 and above | 56 |
| 10 and above | 86 |
| 0 and above | 100 |
How many students have scored marks 20 or more but less than 40?
Option 1: 31
Option 2: 56
Option 3: 44
Option 4: 100
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