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प्रश्न
Write the median class for the following frequency 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 |
उत्तर
We are given the following table.
| Class Interval | Frequency | Cumulative Frequency |
| 0−10 | 5 | 5 |
| 10−20 | 8 | 13 |
| 20−30 | 7 | 20 |
| 30−40 | 12 | 32 |
| 40−50 | 28 | 60 |
| 50−60 | 20 | 80 |
| 60−70 | 10 | 90 |
| 70−80 | 10 | 100 |
| N = 100 |
Here, N = 100
The cumulative frequency just greater than 50 is 60.
So, the median class is 40−50.
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संबंधित प्रश्न
Find the median of the following data by making a ‘less than ogive’.
| Marks | 0 - 10 | 10-20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80-90 | 90-100 |
| Number of Students | 5 | 3 | 4 | 3 | 3 | 4 | 7 | 9 | 7 | 8 |
The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches:
| Number of Wickets | Less than 15 | Less than 30 | Less than 45 | Less than 60 | Less than 75 | Less than 90 | Less than 105 | Less than 120 |
| Number of bowlers | 2 | 5 | 9 | 17 | 39 | 54 | 70 | 80 |
Draw a ‘less than type’ ogive from the above data. Find the median.
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 |
From the following frequency, prepare the ‘more than’ ogive.
| Score | Number of candidates |
| 400 – 450 | 20 |
| 450 – 500 | 35 |
| 500 – 550 | 40 |
| 550 – 600 | 32 |
| 600 – 650 | 24 |
| 650 – 700 | 27 |
| 700 – 750 | 18 |
| 750 – 800 | 34 |
| Total | 230 |
Also, find the median.
From the following data, draw the two types of cumulative frequency curves and determine the median:
| Marks | Frequency |
| 140 – 144 | 3 |
| 144 – 148 | 9 |
| 148 – 152 | 24 |
| 152 – 156 | 31 |
| 156 – 160 | 42 |
| 160 – 164 | 64 |
| 164 – 168 | 75 |
| 168 – 172 | 82 |
| 172 – 176 | 86 |
| 176 – 180 | 34 |
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.
The median of a given frequency distribution is found graphically with the help of
The arithmetic mean of the following frequency distribution is 53. Find the value of k.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 12 | 15 | 32 | k | 13 |
The marks obtained by 100 students of a class in an examination are given below.
| Mark | No. of Student |
| 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 'a less than' type cumulative frequency curves (ogive). Hence find the median.
The following table shows the cumulative frequency distribution of marks of 800 students in an examination:
| Marks | Number of students |
| Below 10 | 10 |
| Below 20 | 50 |
| Below 30 | 130 |
| Below 40 | 270 |
| Below 50 | 440 |
| Below 60 | 570 |
| Below 70 | 670 |
| Below 80 | 740 |
| Below 90 | 780 |
| Below 100 | 800 |
Construct a frequency distribution table for the data above.
