Case Study Question 07

Mathematics

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.Case study Statistics 07
Details of which are given in the following table.

Mileage (km/charge)100-120120-140140-160160-180
Number of scooters7121813

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 :

Class intervalClass Mark (`x_{i}`)Frequency (`f_{i}`)`x_{i}f_{i}`Cumulative Frequency (c.f.)
100-12011077707
120-14013012156019
140-16015018270037
160-18017013221050
Total 507240 

Clearly, average mileage = `\frac{7240}{50}`
= 144.8 km/charge

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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