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प्रश्न
The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its ______.
विकल्प
Mean
Median
Mode
All the three above
उत्तर
The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its median.
Explanation:
Since, the intersection point of less than ogive and more than ogive gives the median on the abscissa
The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its
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The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
| Weight (in kg) | 40−45 | 45−50 | 50−55 | 55−60 | 60−65 | 65−70 | 70−75 |
| Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
The following is the distribution of the size of certain farms from a taluka (tehasil):
| Size of Farms (in acres) |
Number of Farms |
| 5 – 15 | 7 |
| 15 – 25 | 12 |
| 25 – 35 | 17 |
| 35 – 45 | 25 |
| 45 – 55 | 31 |
| 55 – 65 | 5 |
| 65 – 75 | 3 |
Find median size of farms.
Compute the median for the following data:
| Marks | No. of students |
| More than 150 | 0 |
| More than 140 | 12 |
| More than 130 | 27 |
| More than 120 | 60 |
| More than 110 | 105 |
| More than 100 | 124 |
| More than 90 | 141 |
| More than 80 | 150 |
The following table shows the daily wages of workers in a factory:
| Daily wages in (Rs) | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 |
| Number of workers | 40 | 32 | 48 | 22 | 8 |
Find the median daily wage income of the workers.
The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.
| Class (No. of mangoes) |
Frequency (No. of trees) |
Cumulative frequency (less than) |
| 50-100 | 33 | 33 |
| 100-150 | 30 | 63 |
| 150-200 | 90 | 153 |
| 200-250 | 80 | 233 |
| 250-300 | 17 | 250 |
Obtain the median for the following frequency distribution:
| x : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| f : | 8 | 10 | 11 | 16 | 20 | 25 | 15 | 9 | 6 |
The median of the following observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.
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| 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:
Will the median class and modal class of grouped data always be different? Justify your answer.
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
| Age (in years) | Number of policy holders |
| Below 20 | 2 |
| Below 25 | 6 |
| Below 30 | 24 |
| Below 35 | 45 |
| Below 40 | 78 |
| Below 45 | 89 |
| Below 50 | 92 |
| Below 55 | 98 |
| Below 60 | 100 |
