# Case Study Question 06

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

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 :

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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