Advertisements
Advertisements
प्रश्न
The measurements (in mm) of the diameters of the head of the screws are given below:
| Diameter (in mm) | No. of Screws |
| 33 — 35 | 10 |
| 36 — 38 | 19 |
| 39 — 41 | 23 |
| 42 — 44 | 21 |
| 45 — 47 | 27 |
Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.
उत्तर
Let A be the assumed mean.
A is taken as the class mark of the middle class.
Hence, let us take 40 as the assumed mean.
Then A = 40 and deviation di = xi – A = xi – 40
| Diameter | Class | Deviations | Number of | fidi |
| (in mm) | marks | di=xi-A | Screws | - |
| - | xi | di=xi-40 | fi | - |
| 33-35 | 34 | -6 | 10 | -60 |
| 36-38 | 37 | -3 | 19 | -57 |
| 39-41 | 40=A | 0 | 23 | 0 |
| 42-44 | 43 | 3 | 21 | 63 |
| 45-47 | 46 | 6 | 27 | 162 |
| Total | - | - | ∑fi=100 | ∑fidi=108 |
Here,∑fidi=108, ∑fi=100
`bard=(Sigmaf_id_i)/(Sigmaf_i)=108/100=1.08`
`barx=A+bard`
=40+1.08
=41.08
Thus, the mean diameter of the screw heads is 41.08 mm.
संबंधित प्रश्न
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
| Literacy rate (in %) | 45 − 55 | 55 − 65 | 65 − 75 | 75 − 85 | 85 − 95 |
| Number of cities | 3 | 10 | 11 | 8 | 3 |
The arithmetic mean of the following data is 14. Find the value of k
| x1 | 5 | 10 | 15 | 20 | 25 |
| f1 | 7 | k | 8 | 4 | 5 |
The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:
| No. of students absent (x) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| No. of days (f) | 1 | 4 | 10 | 50 | 34 | 15 | 4 | 2 |
Find the mean number of students absent per day.
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
| Classes | 25 - 29 | 30 - 34 | 35 - 39 | 40 - 44 | 45 - 49 | 50 - 54 | 55 - 59 |
| Frequency | 14 | 22 | 16 | 6 | 5 | 3 | 4 |
If the mean of 5 observation x, x + 2, x + 4, x + 6and x + 8 , find the value of x.
If the mean of the following frequency distribution is 24, find the value of p.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 3 | 4 | p | 3 | 2 |
Which measure of central tendency is given by the x-coordinate of the point of intersection of the 'more than' ogive and 'less than' ogive?
If the arithmetic mean of x, x + 3, x + 6, x + 9, and x + 12 is 10, the x =
In the formula
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.
In a small scale industry, salaries of employees are given in the following distribution table:
|
Salary (in Rs.) |
4000 - 5000 |
5000 - 6000 |
6000 - 7000 |
7000 - 8000 |
8000 - 9000 |
9000 - 10000 |
|
Number of employees |
20 | 60 | 100 | 50 | 80 | 90 |
Then the mean salary of the employee is?
A car travels from city A to city B, 120 km apart at an average speed of 50km/h. It then makes a return trip at an average speed of 60km/h. It covers another 120km distance at an average speed of 40km/h. The average speed over the entire 360km will be ______.
The mean of the following distribution is
| xi | 10 | 13 | 16 | 19 |
| fi | 2 | 5 | 7 | 6 |
In the formula `barx = a + (f_i d_i)/f_i`, for finding the mean of grouped data di’s are deviations from a of ______.
The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below:
| Mileage (km/l) | 10 – 12 | 12 – 14 | 14 – 16 | 16 – 18 |
| Number of cars | 7 | 12 | 18 | 13 |
Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?
Find the mean of the following data using assumed mean method:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 8 | 7 | 10 | 13 | 12 |
Find the mean of the following frequency distribution:
| Class | 1 – 5 | 5 – 9 | 9 – 13 | 13 – 17 |
| Frequency | 4 | 8 | 7 | 6 |
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:
| Length (in mm) | Number of leaves |
| 118−126 | 3 |
| 127–135 | 5 |
| 136−144 | 9 |
| 145–153 | 12 |
| 154–162 | 5 |
| 163–171 | 4 |
| 172–180 | 2 |
Find the mean length of the leaves.
