### Solve the following : Calculate of Q3, D5, and P35 for the given data Income (in lakhs ) 1 2 3 4 5 6 No. of family 2 5 20 25 15 12 - Economics

#### QUESTION

Solve the following :

Calculate of Q3, D5, and P35 for the given data

 Income (in lakhs ₹) 1 2 3 4 5 6 No. of family 2 5 20 25 15 12

#### SOLUTION

Arrange the data of the income in ascending order.
(i.e. from lowest number to highest as shown below) and the out the cumulative frequency.

 Income (in lakhs RS) no. of family cumulative frequency(cf) 1 2 2 2 5 7 3 20 27 4 25 52 5 15 67 6 12 79 N = 79

Q3 = Size of 3${\left(\frac{n+1}{4}\right)}^{\text{th observation}}$

= size of 3${\left(\frac{79+1}{4}\right)}^{\text{th observation}}$

= size of 3${\left(\frac{80}{4}\right)}^{\text{th observation}}$

= size of 3 ${\left(20\right)}^{\text{th observation}}$

= size of 60th observation  lies in cf 67

Hence, quartile value = Rs .5 lakhs Q3 = Rs. 5 Lakhs

D= size of 5${\left(\frac{n+1}{10}\right)}^{\text{th observation}}$

=size of 5${\left(\frac{79+1}{10}\right)}^{\text{th observation}}$

= size of 5${\left(\frac{80}{10}\right)}^{\text{th observation}}$

= size of 5${\left(8\right)}^{\text{th observation}}$

= size of ${\left(40\right)}^{\text{th observation}}$

Size of 40th observation lies in cf 52 , hence decile value =Rs. 4 Lakhs

D5 =Rs. 4 Lakhs

P35 =Size of 35${\left(\frac{n+1}{100}\right)}^{\text{th observation}}$

P35 =Size of 35${\left(\frac{79+1}{100}\right)}^{\text{th observation}}$

P35 =Size of 35${\left(\frac{80}{100}\right)}^{\text{th observation}}$

=Size of 35 ${\left(0.80\right)}^{\text{th observation}}$

=Size of 28th observation lies in cf 52

Hence, percentile value = Rs.4 lakhs P35 = Rs. 4 lakhs.