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प्रश्न
250 apples of a box were weighed and the distribution of masses of the apples is given in the following table:
| Mass (in grams) |
80 – 100 | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 |
| Number of apples |
20 | 60 | 70 | x | 60 |
Find the modal mass of the apples.
उत्तर
Mode = `l + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx h` ...(1)
Where l = lower class limit of modal class = 12
Modal class is (120 – 140), Since it consists highest frequency
∴ l = 120
h = class size = 20
f1 = frequency of modal class = 70
f0 = frequency of class preceding the modal class = 60
f2 = frequency of class succeeding the modal class = 40
On putting these values in (1), we get
Modal mass or mode
= `120 + ((70 - 60)/(2 xx 70 - 60 - 40)) xx 20`
= `120 + 10/40 xx 20`
= `120 + 10/2`
= 120 + 5
= 125
संबंधित प्रश्न
Find the mode of the following distribution.
| Class-interval: | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency: | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |
Find the mode of the following distribution.
| Class-interval: | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |
| Frequency: | 30 | 45 | 75 | 35 | 25 | 15 |
The agewise participation of students in the annual function of a school is shown in the following distribution.
| Age (in years) | 5 - 7 | 7 - 9 | 9 - 11 | 11 – 13 | 13 – 15 | 15 – 17 | 17 – 19 |
| Number of students | x | 15 | 18 | 30 | 50 | 48 | x |
Find the missing frequencies when the sum of frequencies is 181. Also find the mode of the data.
Find the mode of the given data: 3.1, 3.2, 3.3, 2.1, 1.3, 3.3, 3.1
The mode of the following data is:
| xi | 10 | 14 | 18 | 21 | 25 |
| fi | 10 | 15 | 7 | 9 | 9 |
Find the mode of the following data.
| Class interval | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequency | 7 | 13 | 14 | 5 | 11 |
There are lottery tickets labelled numbers from 1 to 500. I want to find the number which is most common in the lottery tickets. What quantity do I need to use?
Which of the following is not a measure of central tendency?
For ‘more than ogive’ the x-axis represents ______.
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`.
