Question

1. a set of data has an interquartile range of 20 and a lower quartile of 6. if the data are symmetrical, what is the value of the median?

2. if you double the value of each value in a set of data, what happens to the value of the coefficient of variation? justify your answer.

Answer 1

Answer:

Step-by-step explanation:

Given Q1 as the lower quartile, Q3 the upper quartile and Q2 the second quartile :

Interquartile range = Q3 - Q4

We substitute from the question above :

20 = Q3 - 6

Q3 = 26

Since the data is the data is symmetrical the median lies between the upper and lower quartile.

Q2(median) = (Q3 + Q1) /2 = (26 + 6)/2

= 32/2 = 16

The median = 16

2) When the data is doubled the standard deviation and the mean are also doubled. As we know coefficient of variation is the ratio between the standard deviation and the mean.

The Coefficient of variation remains constant therefore even when data is doubled.