Question

From the monthly income (in Rs.) of 10 families given below, calculate quartile deviation.
145, 367, 268, 73, 185, 619, 280, 115, 870, 315

Answer 1

Answer:

Quartile deviation = 146.25

Step-by-step explanation:

First Quartile Q1 = $\frac{n+1}{4}th$ term.

or, $\frac{10+1}{4}th$ term.

or, 2.75th term.

Sorted Data – 73, 115, 145, 185, 268, 280, 315, 367, 619, 870

2nd term + 0.75 × (3rd term – 2nd term)

or, 115 + 0.75 * (145 - 115)

or, 137.5

Third Quartile Q3 = $\frac{3}{4}* (n+1)$th term

or, 33/4 =  8.25th term

= 8th term + 0.25 × (9th term – 8th term)

or, 367 + 0.25 * (619 - 367)

or, 367 + 63 = 430.

Quartile Deviation = Semi-Inter Quartile Range (The difference of third quartile and first quartile)

or, (430 - 137.5) / 2

or, 146.25 [Ans]