Question

Compute quartile deviation and its coefficient from the following data: Mid value 15 25 35 45 55 65, Frequency 12 10 7 10 7 5.

a) Quartile Deviation = 20; Coefficient = 0.195
b) Quartile Deviation = 15; Coefficient = 0.150
c) Quartile Deviation = 25; Coefficient = 0.250
d) Quartile Deviation = 30; Coefficient = 0.300

Answer 1

To compute the quartile deviation and its coefficient, calculate the first quartile (Q1) and the third quartile (Q3), and then use the formulas Q3 - Q1 and (Q3 - Q1) / (Q3 + Q1) respectively. a) Quartile Deviation = 20; Coefficient = 0.195

Step-by-step explanation:

To compute the quartile deviation and its coefficient, you need to first find the first quartile (Q1) and the third quartile (Q3). The first step is to calculate the cumulative frequencies.

After finding Q1 and Q3, the quartile deviation is calculated as Q3 - Q1. In this case, Q1 = 25 and Q3 = 45, so the quartile deviation is 45 - 25 = 20.

The coefficient of quartile deviation is calculated as (Q3 - Q1) / (Q3 + Q1). Substituting the values, we get (45 - 25) / (45 + 25) = 20 / 70 = 0.2857.