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 − 2000 2000 − 3000 3000 − 4000 4000 − 5000 5000 − 6000 6000 − 7000 7000 − 8000 8000 − 9000		8 10 15 18 22 8 6 3

Compute the median income-tax.

Answer 1

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, … in the first row and 8, 18, … 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.