# Case Study Question 07

## Chapter 14: Statistics

### Class 10

Read the following passage carefully and answer the following questions:

Electric Scooter

Manufacturing Company An electric scooter manufacturing company wants to declare the mileage of their electric scooters. For this, they recorded the mileage (km/charge) of 50 scooters of the same model.
Details of which are given in the following table.

Question.1.
The average mileage is

(a) 140 km/charge
(b) 150 km/charge
(c) 130 km/charge
(d) 144.8 km/charge

(d) : Given frequency distribution table can be drawn as :

Question.2.
The modal value of the given data is

(a) 150
(b) 150.91
(c) 145.6
(d) 140.9

(b) : Since, highest frequency is 18, therefore, modal class is 140-160.
Here, l = 140, f_{1} = 18, f_{0} = 12, f_{2} = 13, h = 20
\therefore Mode = 140+\frac{18-12}{36-12-13}\times20
= 140+\frac{6}{11}\times20
= 140+\frac{120}{11}
= 140+10.91
= 150.91

Question.3.
The median value of the given data is

(a) 140
(b) 146.67
(c) 130
(d) 136.6

(b) :\frac{N}{2}=\frac{50}{2}=25 and the corresponding class whose cumulative frequency is just greater than 25 is
140-160.
Here, l = 140, c.f. = 19, h = 20 and f = 18
\therefore Median = l+\left(\frac{\frac{N}{2}-c.f.}{f}\right)\times h
= 140+\left(\frac{25-19}{18}\right)\times 20
= 140+\frac{60}{9}
= 146.67

Question.4.
Assumed mean method is useful in determining the

(a) Mean
(b) Median
(c) Mode
(d) All of these

(a) : Assumed mean method is useful in determining the mean.

Question.5.
The manufacturer can claim that the mileage for his scooter is

(a) 144 km/charge
(b) 155 km/charge
(c) 165 km/charge
(d) 175 km/charge

(a) : Since, Mean = 144.8, Mode = 150.91 and Median = 146.67 and minimum of which is 144 approx, therefore manufacturer can claim the mileage for his scooter 144 km/charge

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