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प्रश्न
What is the cumulative frequency of the modal class of the following distribution?
| Class | 3 – 6 | 6 – 9 | 9 – 12 | 12 – 15 | 15 – 18 | 18 – 21 | 21 – 24 |
|
Frequency |
7 | 13 | 10 | 23 | 54 | 21 | 16 |
उत्तर
Here the maximum class frequency is 23, and the class corresponding to this frequency is 12-15.
So, the modal class is 12.15.
Now, to find the cumulative frequency let us put the data in the table given below:
| Class | Frequency` (f_i)` | Cumulative frequency (𝑐𝑓) |
| 3-6 | 7 | 7 |
| 6-9 | 13 | 20 |
| 9-12 | 10 | 30 |
| 12-15 | 23 | 53 |
| 15-18 | 4 | 5 |
| 18-21 | 21 | 78 |
| 21-24 | 16 | 94 |
| Total | `N= Σf_i=94` |
Thus, the cumulative frequency of the modal class is 53.
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संबंधित प्रश्न
During the medical check-up of 35 students of a class, their weights were recorded as follows:
| Weight (in kg | Number of students |
| Less than 38 | 0 |
| Less than 40 | 3 |
| Less than 42 | 5 |
| Less than 44 | 9 |
| Less than 46 | 14 |
| Less than 48 | 28 |
| Less than 50 | 32 |
| Less than 52 | 35 |
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.
Draw a ‘more than’ ogive for the data given below which gives the marks of 100 students.
| Marks | 0 – 10 | 10 – 20 | 20 – 30 | 30 - 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 |
| No of Students | 4 | 6 | 10 | 10 | 25 | 22 | 18 | 5 |
The heights of 50 girls of Class X of a school are recorded as follows:
| Height (in cm) | 135 - 140 | 140 – 145 | 145 – 150 | 150 – 155 | 155 – 160 | 160 – 165 |
| No of Students | 5 | 8 | 9 | 12 | 14 | 2 |
Draw a ‘more than type’ ogive for the above data.
The table given below shows the weekly expenditures on food of some households in a locality
| Weekly expenditure (in Rs) | Number of house holds |
| 100 – 200 | 5 |
| 200- 300 | 6 |
| 300 – 400 | 11 |
| 400 – 500 | 13 |
| 500 – 600 | 5 |
| 600 – 700 | 4 |
| 700 – 800 | 3 |
| 800 – 900 | 2 |
Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.
The marks obtained by 100 students of a class in an examination are given below:
| Marks | Number of students |
| 0 – 5 | 2 |
| 5 – 10 | 5 |
| 10 – 15 | 6 |
| 15 – 20 | 8 |
| 20 – 25 | 10 |
| 25 – 30 | 25 |
| 30 – 35 | 20 |
| 35 – 40 | 18 |
| 40 – 45 | 4 |
| 45 – 50 | 2 |
Draw cumulative frequency curves by using (i) ‘less than’ series and (ii) ‘more than’ series.Hence, find the median.
The following table, construct the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.
| Marks obtained (in percent) | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 |
| Number of Students | 141 | 221 | 439 | 529 | 495 | 322 | 153 |
(a) Convert the given frequency distribution into the continuous form.
(b) Find the median class and write its class mark.
(c) Find the modal class and write its cumulative frequency.
Consider the following frequency distributions
| Class | 65 - 85 | 85 - 105 | 105 - 125 | 125 - 145 | 145 - 165 | 165 - 185 | 185-205 |
| Frequency | 4 | 5 | 13 | 20 | 14 | 7 | 4 |
The difference of the upper limit of the median class and the lower limit of the modal class is?
If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.
If the median of the following frequency distribution is 32.5. Find the values of f1 and f2.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | Total |
| Frequency | f1 | 5 | 9 | 12 | f2 | 3 | 2 | 40 |
For one term, absentee record of students is given below. If mean is 15.5, then the missing frequencies x and y are.
| Number of days | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | TOTAL |
| Total Number of students | 15 | 16 | x | 8 | y | 8 | 6 | 4 | 70 |
