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प्रश्न
The table below shows the daily expenditure on food of 25 households in a locality.
| Daily expenditure (in Rs) | 100 − 150 | 150 − 200 | 200 − 250 | 250 − 300 | 300 − 350 |
| Number of households | 4 | 5 | 12 | 2 | 2 |
Find the mean daily expenditure on food by a suitable method.
उत्तर
To find the class mark (xi) for each interval, the following relation is used:
Let the assumed mean, a = 225
Class size, h = 50
= `u_i = (x_i - a)/h`
= `(x_i - 225)/50`
Taking 225 as the assumed mean (a), di, ui, fiui are calculated as follows.
| Daily expenditure (in Rs) | fi | xi | di = xi − 225 | `u_i=(x_i-225)/50` | fiui |
| 100 − 150 | 4 | 125 | − 100 | − 2 | − 8 |
| 150 − 200 | 5 | 175 | − 50 | − 1 | − 5 |
| 200 − 250 | 12 | 225 | 0 | 0 | 0 |
| 250 − 300 | 2 | 275 | 50 | 1 | 2 |
| 300 − 350 | 2 | 325 | 100 | 2 | 4 |
| Total | 25 | -7 |
From the table, we obtain:
`sumf_i = 25`
`sumf_iu_i = -7`
`"Mean " barx = a+ ((sumf_1u_i)/(sumf_i))xh`
= `225 + ((-7)/25)xx(50)`
= 225 − 14
= 211
Therefore, mean daily expenditure on food is Rs 211.
संबंधित प्रश्न
Consider the following distribution of daily wages of 50 worker of a factory.
|
Daily wages (in Rs) |
100 − 120 |
120 − 140 |
140 −1 60 |
160 − 180 |
180 − 200 |
|
Number of workers |
12 |
14 |
8 |
6 |
10 |
Find the mean daily wages of the workers of the factory by using an appropriate method.
Find the value of p for the following distribution whose mean is 16.6
| x | 8 | 12 | 15 | P | 20 | 25 | 30 |
| f | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
The following table gives the number of children of 150 families in a village. Find the average number of children per family.
| No. of children (x) | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of families (f) | 10 | 21 | 55 | 42 | 15 | 7 |
The following distribution gives the number of accidents met by 160 workers in a factory during a month.
| No. of accidents(x) | 0 | 1 | 2 | 3 | 4 |
| No. of workers (f) | 70 | 52 | 34 | 3 | 1 |
Find the average number of accidents per worker.
The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city. Find the average expenditure (in rupees) per household.
| Expenditure (in rupees) (x1) |
Frequency(f1) |
| 100 - 150 | 24 |
| 150 - 200 | 40 |
| 200 - 250 | 33 |
| 250 - 300 | 28 |
| 300 - 350 | 30 |
| 350 - 400 | 22 |
| 400 - 450 | 16 |
| 450 - 500 | 7 |
Find the mean of each of the following frequency distributions: (5 - 14)
| Class interval | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 |
| Frequency | 6 | 8 | 10 | 9 | 7 |
Find the mean of each of the following frequency distributions
| Class interval | 10 - 30 | 30 - 50 | 50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 |
| Frequency | 5 | 8 | 12 | 20 | 3 | 2 |
For the following distribution, calculate mean using all suitable methods:
| Size of item | 1 - 4 | 4 - 9 | 9 - 16 | 16 - 27 |
| Frequency | 6 | 12 | 26 | 20 |
The mean of following frequency distribution is 54. Find the value of p.
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 7 | p | 10 | 9 | 13 |
Find the mean age from the following frequency distribution:
| Age (in years) | 25 – 29 | 30 – 34 | 35 – 39 | 40 – 44 | 45 – 49 | 50 – 54 | 55 – 59 |
| Number of persons | 4 | 14 | 22 | 16 | 6 | 5 | 3 |
The following table shows the income of farmers in a grape season. Find the mean of their income.
|
Income
(Thousand Rupees)
|
20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Farmers | 10 | 11 | 15 | 16 | 18 | 14 |
There are three dealers A, B and C in Maharashtra. Suppose, the trade of each of them in september 2018 was as shown in the following table.
The rate of GST on each transaction was 5%.
Read the table and answer the questions below it.
| Dealer | GST collected on the sale |
GST paid at the time of purchase |
ITC | Tax paid to the Govt. |
Taxbalance with the Govt. |
| A | Rs.5000 | Rs. 6000 | Rs. 5000 | Rs. 0 | Rs. 1000 |
| B | Rs 5000 | Rs. 4000 | Rs. 4000 | Rs. 1000 | Rs. 0 |
| C | Rs.5000 | Rs. 5000 | Rs. 5000 | Rs. 0 | Rs. 0 |
(i) How much amount did the dealer A get by sale ?
(ii) For how much amount did the dealer B buy the articles ?
(iii) How much is the balance of CGST and SGST left with the government that was paid by A ?
The arithmetic mean of 1, 2, 3, ... , n is
The weekly wages of 120 workers in a factory are shown in the following frequency distribution table. Find the mean of the weekly wages.
|
Weekly wages
(Rupees)
|
0 - 2000 | 2000 - 4000 | 4000 - 6000 | 6000 - 8000 |
| No. of workers | 15 | 35 | 50 | 20 |
In X standard, there are three sections A, B and C with 25, 40 and 35 students respectively. The average marks of section A is 70%, section B is 65% and of section C is 50%. Find the average marks of the entire X standard.
The average score of boys in an examination of a school is 71 and of girls is 73. The averages score of school in that examination is 71.8. Find the ratio of the number of boys between number of girls appeared in the examination.
Find the mean of the following distribution:
| x | 4 | 6 | 9 | 10 | 15 |
| f | 5 | 10 | 10 | 7 | 8 |
The following table gives the number of pages written by Sarika for completing her own book for 30 days:
| Number of pages written per day |
16 – 18 | 19 – 21 | 22 – 24 | 25 – 27 | 28 – 30 |
| Number of days | 1 | 3 | 4 | 9 | 13 |
Find the mean number of pages written per day.
The daily income of a sample of 50 employees are tabulated as follows:
| Income (in Rs) |
1 – 200 | 201 – 400 | 401 – 600 | 601 – 800 |
| Number of employees |
14 | 15 | 14 | 7 |
Find the mean daily income of employees.
