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प्रश्न
Calculate the median of the following distribution:
| No. of goals | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 2 | 4 | 7 | 6 | 8 | 3 |
उत्तर
The given variates (no. of goals) are already in ascending order. We construct the cumulative frequency table as under:
| Variate (No. of goals) | Frequency (No. of matches) |
Cumulative frequency |
| 0 | 2 | 2 |
| 1 | 4 | 6 |
| 2 | 7 | 13 |
| 3 | 6 | 19 |
| 4 | 8 | 27 |
| 5 | 3 | 30 |
Here, n = 30, which is even.
∴ Median
= `("n"/2 "th observation" + ("n"/2 + 1)"th observation")/(2)`
= `(15"th observation" + 16"th observation")/(2)`
= `(3 + 3)/(2)` = 3.
(∵ All observation form 14th to 19th are equal, each = 3).
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संबंधित प्रश्न
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.
An incomplete distribution is given below:
| Variable: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency: | 12 | 30 | - | 65 | - | 25 | 18 |
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
Write the median class of the following distribution:
| Class-interval: | 0−10 | 10−20 | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 |
| Frequency: | 4 | 4 | 8 | 10 | 12 | 8 | 4 |
Below is the given frequency distribution of words in an essay:
| Number of words | Number of Candidates |
| 600 - 800 | 12 |
| 800 - 1000 | 14 |
| 1000 - 1200 | 40 |
| 1200 - 1400 | 15 |
| 1400 - 1600 | 19 |
Find the mean number of words written.
Pocket expenses of a class in a college are shown in the following frequency distribution:
| Pocket expenses |
0 - 200 |
200 - 400 |
400 - 600 |
600 - 800 |
800 - 1000 |
1000 - 1200 |
1200 - 1400 |
| Number of students | 33 | 74 | 170 | 88 | 76 | 44 | 25 |
Then the median for the above data is?
Consider the following frequency distribution:
| Class | 0 – 5 | 6 – 11 | 12 – 17 | 18 – 23 | 24 – 29 |
| Frequency | 13 | 10 | 15 | 8 | 11 |
The upper limit of the median class is:
Find the values of a and b, if the sum of all the frequencies is 120 and the median of the following data is 55.
| Marks | 30 – 40 | 40 – 50 | 50 –60 | 60 – 70 | 70 –80 | 80 – 90 |
| Frequency | a | 40 | 27 | b | 15 | 24 |
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately ______.
The median of first seven prime numbers is ______.
A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
| Family size | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 |
| Numbers of Families | 7 | 8 | 2 | 2 | 1 |
Find the median of this data.
