Advertisements
Advertisements
Question
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 |
Solution
|
Class
(Milk sold in litres) |
Class Mark xi |
Frequency (Number of customers) fi |
Class mark × Frequency fixi |
| 1 – 2 | 1.5 | 17 | 25.5 |
| 2 – 3 | 2.5 | 13 | 32.5 |
| 3 – 4 | 3.5 | 10 | 35 |
| 4 – 5 | 4.5 | 7 | 31.5 |
| 5 – 6 | 5.5 | 3 | 16.5 |
| Total | – | `sumf_i` = 50 | `sumf_i x_i` = 141 |
Mean = `(sumf_i x_i)/(sumf_i)`
= `141/50`
= 2.82 litres
Hence, the mean of the milk sold is 2.82 litres.
APPEARS IN
RELATED QUESTIONS
The following data shows the number of students using different modes of transport:
| Modes of Transport | Number of Students |
| Bicycle | 140 |
| Bus | 100 |
| Walk | 70 |
| Train | 40 |
| Car | 10 |
From this table, find the central angle (θ) for the Mode of Transport ‘Bus’.
In the following table, the toll paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.
| Toll (Rupees) | 300 - 400 | 400 - 500 | 500 - 600 | 600 - 700 | 700 - 800 |
| No. of vehicles | 80 | 110 | 120 | 70 | 40 |
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 |
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 |
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 |
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?
Use the table given below to find:
(a) The actual class limits of the fourth class.
(b) The class boundaries of the sixth class.
(c) The class mark of the third class.
(d) The upper and lower limits of the fifth class.
(e) The size of the third class.
| Class Interval | Frequency |
| 30 - 34 | 7 |
| 35 - 39 | 10 |
| 40 - 44 | 12 |
| 45 - 49 | 13 |
| 50 - 54 | 8 |
| 55 - 59 | 4 |
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 |
