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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 |
Compare the modal ages of two groups of students appearing for an entrance test:
| Age (in years): | 16-18 | 18-20 | 20-22 | 22-24 | 24-26 |
| Group A: | 50 | 78 | 46 | 28 | 23 |
| Group B: | 54 | 89 | 40 | 25 | 17 |
Heights of students of class X are givee in the flowing frequency distribution
| Height (in cm) | 150 – 155 | 155 – 160 | 160 – 165 | 165 – 170 | 170 - 175 |
| Number of students | 15 | 8 | 20 | 12 | 5 |
Find the modal height.
Also, find the mean height. Compared and interpret the two measures of central tendency.
Compute the mode from the following data:
| Class interval | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 | 26 – 30 | 31 – 35 | 36 – 40 | 41 – 45 | 46 – 50 |
| Frequency | 3 | 8 | 13 | 18 | 28 | 20 | 13 | 8 | 6 | 4 |
The following table give the marks scored by students in an examination:
| Marks | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 |
| No. of students | 3 | 7 | 15 | 24 | 16 | 8 | 5 | 2 |
(i) Find the modal group
(ii) Which group has the least frequency?
If xi's are the midpoints of the class intervals of grouped data, fi's are the corresponding frequencies and `barx` is the mean, then `sum(f_ix_i-barx)` is equal to ______.
The weight of coffee in 70 packets are shown in the following table:
| Weight (in g) | Number of packets |
| 200 – 201 | 12 |
| 201 – 202 | 26 |
| 202 – 203 | 20 |
| 203 – 204 | 9 |
| 204 – 205 | 2 |
| 205 – 206 | 1 |
Determine the modal weight.
For the following distribution:
| Class | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 |
| Frequency | 10 | 15 | 12 | 20 | 9 |
the upper limit of the modal class is:
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.
