Question

# The table below shows the number of employees of an office, classified according to the income-tax paid by them. Income Tax (Rupees) Number of Employees 1000 âˆ’ 2000 2000 âˆ’ 3000 3000 âˆ’ 4000 4000 âˆ’ 5000 5000 âˆ’ 6000 6000 âˆ’ 7000 7000 âˆ’ 8000 8000 âˆ’ 9000 8 10 15 18 22 8 6 3 Compute the median income-tax.

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Solution

## The given data can be shown as: Income Tax (Rupees) Number of Employee Below 2000 8 Below 3000 18 Below 4000 33 Below 5000 51 Below 6000 73 Below 7000 81 Below 8000 87 Below 9000 90 Let us tabulate the numbers 2000, 3000, â€¦ in the first row and 8, 18, â€¦ in the second row. x 2000 3000 4000 5000 6000 7000 8000 9000 y 8 18 33 51 73 81 87 90 We know that the change in y is proportional to the corresponding change in x. We have to find that value of x for which y = The number 45 is between the numbers y = 33 and y = 51. The corresponding numbers are x = 4000 and x = 5000. Thus, we must have: Thus, the median income tax of the employees of the office is Rs.4666.67.

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