Case Study Question 06

Mathematics

Chapter 14: Statistics

Class 10

Read the following passage carefully and answer the following questions:

Toll Tax Collection

On a particular day, National Highway Authority of India (NHAI) checked the toll tax collection of a particular toll plaza in Rajasthan.Case study Statistics 06

The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.

Toll tax (in Rs.)30-4040-5050-6060-7070-80
Number of Vehicles801101207040

Question.1.
If A is taken as assumed mean, then the possible value of A is

(a) 32
(b) 42
(c) 85
(d) 55

(d) : Let us consider the following table :

Class Class marks (`x_{i}`)`d_{i}=x_{i}-`AFrequency (`f_{i}`)`f_{i}d_{i}`
30-4035-2080-1600
40-5045-10110-1100
50-6055=A01200
60-70651070700
70-80752040800
Total  `\sum f_{i}`=420`\sum f_{i}d_{i}`=`-1200`

Clearly, the possible values of assumed mean (A) are 35, 45, 55, 65, 75.

Question.2.
If `x_{i}`’s denote the class marks and `d_{i}`’s denote the deviation of assumed mean (A) from `x_{i}`’s, then the minimum value of |`d_{i}`| is

(a) –200
(b) –100
(c) 0
(d) 100 

(c) : The values of |`d_{i}`| are 0, 10, 20
Thus, the minimum value of |`d_{i}`| is 0.

Question.3.
The mean of toll tax received by NHAI by assumed mean method is

(a) Rs. 52
(b) Rs. 52.14
(c) Rs. 52.50
(d) Rs. 53.50

(b) : Required Mean = `A+\frac{\sum f_{i}d_{i}}{\sum f_{i}}`
= `55-\frac{1200}{420}`
= Rs. 52.14

Question.4.
The mean of toll tax received by NHAI by direct method is

(a) equal to the mean of toll tax received by NHAI by assumed mean method
(b) greater than the mean of toll tax received by NHAI by assumed mean method
(c) less than the mean of toll tax received by NHAI by assumed mean method
(d) can’t say

(a) : Mean by direct and assumed mean method are always equal. 

Question.5.
The average toll tax received by NHAI in a day, from that particular toll plaza, is

(a) Rs. 21000.60
(b) Rs. 21900.80
(c) Rs. 30000.90
(d) Rs. 21898.80

(d) : Average toll tax received by a vehicle = Rs. 52.14
Total number of vehicles = 420
`\therefore` Average toll tax received in a day = Rs. (52.14 `\times` 420)
= Rs. 21898.80

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