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Question
The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.
Solution
Given, Mode = 75
Modal class = 65 – 80
Frequency of the class preceding the modal class, f0 = 6
Frequency of class succeeding the modal class, f2 = 8
Here, the lower limit of modal class, l = 65 and class size = 15
Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`
⇒ 75 = `65 + ((f_1 - 6)/(2f_1 - 6 - 8)) xx 15`
⇒ 10 = `(f_1 - 6)/(2f_1 - 14) xx 15`
⇒ `20f_1 - 140 = 15f_1 - 90`
⇒ `5f_1` = 50
⇒ `f_1` = 10
Hence, the frequency of modal class `(f_1)` is 10.
RELATED QUESTIONS
Find the mode of the following data:
3, 5, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7, 4
Compute the mode of the following data:
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency | 25 | 16 | 28 | 20 | 5 |
Compute the mode from the following series:
| Size | 45 – 55 | 55 – 65 | 65 – 75 | 75 – 85 | 85 – 95 | 95 – 105 | 105 - 115 |
| Frequency | 7 | 12 | 17 | 30 | 32 | 6 | 10 |
One of the methods of determining mode is ______.
Find the mode of the following frequency distribution:
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
For the following distribution
| Marks | No. of students |
| Less than 20 | 4 |
| Less than 40 | 12 |
| Less than 60 | 25 |
| Less than 80 | 56 |
| Less than 100 | 74 |
| Less than 120 | 80 |
the modal class is?
Find the mode of the following frequency distribution:
| Class: | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |
| Frequency: | 25 | 30 | 45 | 42 | 35 |
The frequency distribution of daily working expenditure of families in a locality is as follows:
| Expenditure in ₹ (x): |
0 – 50 | 50 – 100 | 100 – 150 | 150 – 200 | 200 – 250 |
| No. of families (f): |
24 | 33 | 37 | b | 25 |
If the mode of the distribution is ₹ 140 then the value of b is ______.
The upper limit of the modal class of the given distribution is:
| Height [in cm] | Below 140 | Below 145 | Below 150 | Below 155 | Below 160 | Below 165 |
| Number of girls | 4 | 11 | 29 | 40 | 46 | 51 |
The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity:
| Class (Petrol filled in Liters) |
Frequency (Number of Vehicles) |
| 0.5 - 3.5 | 33 |
| 3.5 - 6.5 | 40 |
| 6.5 - 9.5 | 27 |
| 9.5 - 12.5 | 18 |
| 12.5 - 15.5 | 12 |
Activity:
From the given table,
Modal class = `square`
∴ Mode = `square + [(f_1 - f_0)/(2f_1 -f_0 - square)] xx h`
∴ Mode = `3.5 + [(40 - 33)/(2(40) - 33 - 27)] xx square`
∴ Mode = `3.5 +[7/(80 - 60)] xx 3`
∴ Mode = `square`
∴ The mode of the volume of petrol filled is `square`.
