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Question
Read the following passage and answer the questions given below.
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Electric buses are becoming popular nowadays. These buses have the electricity stored in a battery. Electric buses have a range of approximately 280 km with just charge. These buses are superior to diesel buses as they reduce brake wear and also reduce pollution. 'transport department of a city wants to buy some electric buses for the city. So, the department wants to know the distance travelled by existing public transport buses in a day. The following data shows the distance travelled by 50 existing public transport buses in a day.
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| Daily distance travelled (in km) | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 | 180 – 200 |
| Number of buses | 12 | 14 | 8 | 6 | 10 |
- Find the 'median' distance travelled by a bus.
- Find the 'mean (average)' distance travelled by a bus.
Solution
| Distance (in km) |
No. of Buses `bb((f_i))` |
Mid-point `bb((x_i))` |
`bb(cf)` | `bb(f_ix_i)` |
| 100 – 120 | 12 | 110 | 12 | 1320 |
| 120 – 140 | 14 | 130 | 26 | 1820 |
| 140 – 160 | 8 | 150 | 34 | 1200 |
| 160 – 180 | 6 | 170 | 40 | 1020 |
| 180 – 200 | 10 | 190 | 50 | 1900 |
| N = `sumf_i` = 50 | `sumf_ix_i` = 7260 |
a. Here, N = 50
⇒ `N/2` = 25
So, median class is 120 – 140
Here, l = 120, F = 12, f = 14 and h = 20
Median = `l + ((N/2 - F)/f) xx h`
= `120 + ((25 - 12)/14) xx 20`
= 120 + 18.57
= 138.57
Hence, median distance travelled by the bus is 138.57 km.
b. Mean = `(sumf_ix_i)/(sumf_i)`
= `7260/50`
= 145.2
Hence, mean distance travelled by the bus is 145.2 km.
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