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प्रश्न
The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.
|
No. of bulbs produced
(Thousands) |
30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| No. of factories | 12 | 35 | 20 | 15 | 8 | 7 | 8 |
उत्तर
|
Class
No. of bulbs produced (in thousands) |
Frequency (Number of factories) fi |
Cumulaive frequency (less than) |
| 30 - 40 | 12 | 12 |
| 40 - 50 | 35 | 47→cf |
| 50 - 60 (Median Class) |
20→f | 67 |
| 60 - 70 | 15 | 82 |
| 70 - 80 | 8 | 90 |
| 80 - 90 | 7 | 97 |
| 90 - 100 | 8 | 105 |
| Total | N = 105 |
Here, total frequency = Σfi = N = 105
∴ `"N"/2 = 105/2 = 52.5`
Cumulative frequency which is just greater than (or equal) to 52.5 is 67.
∴ The median class is 50 – 60.
Now, L = 50, f = 20, cf = 47, h = 10.
∴ Media = `"L" + (("N"/2 - "cf")/"f") × h`
`= 50 + ((52.5 - 47)/20) × 10`
`= 50 + ((5.5)/20) × 10`
= 50 + 2.75
= 52.75 thousand lamps
= 52.75 × 1000
= 52750 lamps
Hence, the median of the productions is 52750 lamps.
संबंधित प्रश्न
The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.
| Time (hrs.) | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 |
| No. of students | 7 | 18 | 12 | 10 | 3 |
A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.
| Milk Sold (Litre) | 1 – 2 | 2 – 3 | 3 – 4 | 4 – 5 | 5 – 6 |
| No. of Customers | 17 | 13 | 10 | 7 | 3 |
A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method.
|
Production
(Thousand rupees)
|
25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 | 45 - 50 |
| No. of Customers | 20 | 25 | 15 | 10 | 10 |
A frequency distribution of funds collected by 120 workers in a company for the drought affected people are given in the following table. Find the mean of the funds by 'step deviation' method.
|
Fund (Rupees)
|
0 - 500 | 500 - 1000 | 1000 - 1500 | 1500 - 2000 | 2000 - 2500 |
| No. of workers | 35 | 28 | 32 | 15 | 10 |
The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method.
|
Weekly wages (Rupees)
|
1000 - 2000 | 2000 - 3000 | 3000 - 4000 | 4000 - 5000 |
| No. of workers | 25 | 45 | 50 | 30 |
The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work.
| Daily No. of hours | 8 - 10 | 10 - 12 | 12 - 14 | 14 - 16 |
| Number of workers | 150 | 500 | 300 | 50 |
The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data.
| No. of Mangoes | 50 - 100 | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 |
| No. of trees | 33 | 30 | 90 | 80 | 17 |
The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.
|
Average Speed of
Vehicles (Km/hr) |
60 - 64 | 64 - 69 | 70 - 74 | 75 - 79 | 79 - 84 | 84 - 89 |
| No. of vehicles | 10 | 34 | 55 | 85 | 10 | 6 |
Electricity used by some families is shown in the following table. Find the mode for use of electricity.
| Use of electricity (Unit) | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |
| No. of families | 13 | 50 | 70 | 100 | 80 | 17 |
The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions
| Class (Daily distance travelled in km) |
Continuous Classes |
Frequency (no.of. rickshaws) |
Cumulative frequency less than type |
| 60 – 64 | 59.5 – 64.5 | 10 | 10 |
| 65 – 69 | 64.5 – 69.5 | 34 | 10 + 34 = 44 |
| 70 – 74 | 69.5 – 74.5 | 58 | 44 + 58 = 102 |
| 75 – 79 | 74.5 – 79.5 | 82 | 102 + 82 = 184 |
| 80 – 84 | 79.5 – 84.5 | 10 | 184 + 10 = 194 |
| 85 – 89 | 84.5 – 89.5 | 6 | 194 + 6 = 200 |
- Which is the modal class? Why?
- Which is the median class and why?
- Write the cumulative frequency (C.F) of the class preceding the median class.
- What is the class interval (h) to calculate median?
Find the class mark of class 10 - 20.
The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies:
| Time (hrs.) | No. of. students |
| 0 - 2 | 8 |
| 2 - 4 | 14 |
| 4 - 6 | 18 |
| 6 - 8 | 10 |
| 8 - 10 | 10 |
