Advertisements
Advertisements
Question
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 |
Solution
|
Class (Number of
working hours) |
Frequency (Number of workers) |
Cumulative frequency less than the upper limit |
| 50 - 100 | 33 | 33 |
| 100 - 150 | 30 | 63 |
| 150 - 200 (Median Class) |
90 | 153 |
| 200 - 250 | 80 | 233 |
| 250 - 300 | 17 | 250 |
| N = 250 |
From the above table, we get
L (Lower class limit of the median class) = 150
N (Sum of frequencies) = 250
h (Class interval of the median class) = 50
f (Frequency of the median class) = 90
cf (Cumulative frequency of the class preceding the median class) = 63
Now, Median = `L + ((N/2 - cf)/f) xx h`
= `150 + ((250/2 - 63)/90) xx 50`
= `150 + ((125 - 63)/90) xx 50`
= `150 + (62/9) xx 5`
= `150 + 310/9`
= 150 + 34.44
= 184.44 mangoes
= 184 mangoes
Hence, the median of data is 184 mangoes.
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’.
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 |
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 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 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 |
