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प्रश्न
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?
उत्तर
| Mileage (km/l) |
Class marks `(bb(x_i))` |
Number of cars `(bb(f_i))` |
`bb(f_i x_i)` |
| 10 – 12 | 11 | 7 | 77 |
| 12 – 14 | 13 | 12 | 156 |
| 14 – 16 | 15 | 18 | 270 |
| 16 – 18 | 17 | 13 | 221 |
| Total | `sumf_i = 50` | `sumf_i x_i = 724` |
Here, `sumf_i` = 50
And `sumf_i x_i` = 724
∴ Mean `(barx) = (sumf_i x_i)/(sumf_i)`
= `724/50`
= 14.48
Hence, mean mileage is 14.48 km/l.
No, the manufacture is claiming mileage 1.52 km/l more than average mileage.
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| concentration of SO2 (in ppm) | Frequency |
| 0.00 − 0.04 | 4 |
| 0.04 − 0.08 | 9 |
| 0.08 − 0.12 | 9 |
| 0.12 − 0.16 | 2 |
| 0.16 − 0.20 | 4 |
| 0.20 − 0.24 | 2 |
Find the mean concentration of SO2 in the air.
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| x | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | P | 8 | 4 |
Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.
| No. of heads per toss | No. of tosses |
| 0 | 38 |
| 1 | 144 |
| 2 | 342 |
| 3 | 287 |
| 4 | 164 |
| 5 | 25 |
| Total | 1000 |
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 | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 |
| Frequency | 7 | 5 | 10 | 12 | 6 |
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| Class | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |
| Frequency | 5 | f1 | 10 | f2 | 7 | 8 |
The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is ₹ 18 , find the missing frequency f.
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11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
| Number of children | 7 | 6 | 9 | 13 | f | 5 | 4 |
The daily expenditure of 100 families are given below. Calculate `f_1` and `f_2` if the mean daily expenditure is ₹ 188.
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Expenditure (in Rs) |
140-160 | 160-180 | 180-200 | 200-220 | 220-240 |
|
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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 |
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| Number of match sticks | Number of boxes |
| 35 | 6 |
| 36 | 10 |
| 37 | 18 |
| 38 | 25 |
| 39 | 21 |
| 40 | 12 |
| 41 | 8 |
(i) Calculate correct to one decimal place, the mean number of match sticks per box.
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