Case Study Question 05

Mathematics

Chapter 14: Statistics

Class 10

Read the following passage carefully and answer the following questions:

Distance Analysis of Public Transport Buses

Transport department of a city wants to buy some Electric buses for the city. For which they want to analyse the distance travelled by existing public transport buses in a day.
The following data shows the distance travelled by 60 existing public transport buses in a day.Case study Statistics 05

Daily distance travelled (in km)200-209210-219220-229230-239240-249
Number of buses41426106

Question.1.
The upper limit of a class and lower limit of its succeeding class is differ by

(a) 9
(b) 1
(c) 10
(d) none of these

(b) : The upper limit of a class and the lower class of its succeeding class differ by 1.

Question.2.
The median class is

(a) 229.5-239.5
(b) 230-239
(c) 220-229
(d) 219.5-229.5

(d) : Here, class intervals are in inclusive form. So, we first convert them in exclusive form. The frequency distribution table in exclusive form is as follows :

Class intervalFrequency (`f_{i}`)Cumulative Frequency (c.f.)
199.5-209.544
209.5-219.51418
219.5-229.52644
229.5-239.51054
239.5-249.5660

Here, `\sum f_{i}` i.e., N = 60
⇒ `\frac{N}{2}=30`
Now, the class interval whose cumulative frequency is just greater than 30 is 219.5 – 229.5.
`\therefore` Median class is 219.5 – 229.5.

Question.3.
The cumulative frequency of the class preceding the median class is

(a) 14
(b) 18
(c) 26
(d) 10

(b) : Clearly, the cumulative frequency of the class preceding the median class is 18.

Question.4.
The median of the distance travelled is

(a) 222 km
(b) 225 km
(c) 223 km
(d) none of these

(d) : Median = `l+\left[ \frac{\frac{N}{2}-c.f.}{f}\right] \times h`
= `219.5+\left[ \frac{30-18}{26}\right] \times 10`
= `219.5+\left[ \frac{12\times10}{26}\right]`
= 219.5 + 4.62
= 224.12
`\therefore` Median of the distance travelled is 224.12 km

Question.5.
If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

(a) 225 km
(b) 220 km
(c) 230.29 km
(d) 224.29 km

(d) : We know, Mode = 3 Median – 2 Mean
`\therefore` Mean = `\frac{1}{2}`(3 Median – Mode)
= `\frac{1}{2}`(672.36-223.78)
= 224.29 km

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