Question

Read the following passage and answer the questions given below.

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.

 

Daily distance travelled (in km)	100 – 120	120 – 140	140 – 160	160 – 180	180 – 200
Number of buses	12	14	8	6	10

1. Find the 'median' distance travelled by a bus.
2. Find the 'mean (average)' distance travelled by a bus.

Answer 1

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.