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.
The following table shows the toll tax paid by drivers and the number of vehicles on that particular day.
Toll tax (in Rs.)  3040  4050  5060  6070  7080 
Number of Vehicles  80  110  120  70  40 
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}`A  Frequency (`f_{i}`)  `f_{i}d_{i}` 

3040  35  20  80  1600 
4050  45  10  110  1100 
5060  55=A  0  120  0 
6070  65  10  70  700 
7080  75  20  40  800 
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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