Question

The income tax paid by workers of a certain organisation is given in the table.

$\begin{array}{cc}\text{Income tax (Rs)}& \text{No. of workers}\\ 1000-2000& 8\\ 2000-3000& 10\\ 3000-4000& 15\\ 4000-5000& 18\\ 5000-6000& 8\end{array}$

Find the Median Tax paid by them.

• A. 3766.67
• B. 3480.22
• C. 3225
• D. 3005.55

Answer 1

The correct option is A

3766.67

The cumulative frequency table can be drawn as :

$\begin{array}{cc}\text{Income tax (Rs)}& \text{No. of workers(Cumulative)}\\ <2000& 8\\ <3000& 18\\ <4000& 33\\ <5000& 51\\ <6000& 59\end{array}$

N = 59 (An odd number)

Median = $\frac{(59+1)}{2}th$ observation = 30th observation.

So, the Median class is 3000 - 4000.

We know that there are 15 people from the 18th to the 33rd person whose income is between ₹3000 and ₹4000.

However, we do not know their individual incomes.

We will divide ₹1000 from ₹3000 to ₹4000 into 15 equal parts and assume that one person is in each subdivision.

We will assume that the tax paid by each person in a subdivision is the mid - value of the subdivision.

So, the tax paid by the 19th person is the mid value of ₹3000 and ₹$3000\frac{1000}{15}$, that is ₹$3000\frac{1000}{30}$

So, from the 19th person to the 30th person, there are 11 people.

If the 19th term of the AP is $3000\frac{1000}{30}$ and the common difference is $\frac{1000}{15}$,

Then the 30th term = $3000\frac{1000}{30}$ + $11\times \frac{1000}{15}$

= $3000+\frac{1000+22000}{30}$

= $3000+\frac{23000}{30}$

= 3000 + 766.67

= ₹3766.67