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प्रश्न
The following table gives the wages of worker in a factory:
| Wages in ₹ | 45 - 50 | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |
| No. of Worker's | 5 | 8 | 30 | 25 | 14 | 12 | 6 |
Calculate the mean by the short cut method.
उत्तर
| Class Interval | Frequency `f_i` |
Observation (mid value) `x_i` |
`d_i = x_i - A` | `f_id_i` |
| 45 - 50 | 5 | 47·5 | -15 | -75 |
| 50 - 55 | 8 | 52·5 | -10 | -80 |
| 55 - 60 | 30 | 57·5 | -5 | -150 |
| 60 - 65 | 25 | 62·5 = A | 0 | 0 |
| 65 - 70 | 14 | 67·5 | 5 | 70 |
| 70 - 75 | 12 | 72·5 | 10 | 120 |
| 75 - 80 | 6 | 77·5 | 15 | 90 |
| `sumf_i` = 100 | `sum f_i d_i` = -25 |
Mean `bar"X" = "A" + (sumf_i d_i)/(sumf_i)`
= `62·5 + (-25)/(100)` = 62·25.
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संबंधित 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’.
If the mean of the following distribution is 27, find the value of p.
| Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequency | 8 | p | 12 | 13 | 10 |
The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method .
| Literacy rate(%) |
45 – 55 | 55 – 65 | 65 – 75 | 75 – 85 | 85 – 95 |
| Number of cities |
4 | 11 | 12 | 9 | 4 |
Find the arithmetic mean of the following frequency distribution using step-deviation method:
| Age (in years) | 18 – 24 | 24 – 30 | 30 – 36 | 36 – 42 | 42 – 48 | 48 – 54 |
| Number of workers | 6 | 8 | 12 | 8 | 4 | 2 |
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 |
Define mean.
If the mean of 6, 7, x, 8, y, 14 is 9, then ______.
The measurements (in mm) of the diameters of the head of the screws are given below :
| Diameter (in mm) | no. of screws |
| 33 - 35 | 9 |
| 36 - 38 | 21 |
| 39 - 41 | 30 |
| 42 - 44 | 22 |
| 45 - 47 | 18 |
Calculate the mean diameter of the head of a screw by the ' Assumed Mean Method'.
If mean = (3median - mode) . k, then the value of k is ______.
An analysis of particular information is given in the following table.
| Age Group | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency | 2 | 5 | 6 | 5 | 2 |
For this data, mode = median = 25. Calculate the mean. Observing the given frequency distribution and values of the central tendency interpret your observation.
