Question

What is the coefficient of the range 5, 2, 3, 4, 6, 8 and 10?
a. $\dfrac{2}{3}$
b. $\dfrac{1}{3}$
c. $\dfrac{3}{5}$
d. $\dfrac{1}{2}$

Answer 1

Hint: Coefficient of the range is a relative measure of dispersion and is based on the value of the range. It is also called the range coefficient of dispersion. Do not confuse Range and Coefficient of Range. (Read Note for more information)

Complete step-by-step answer:

Given that, Data: 5, 2, 3, 4, 6, 8 and 10.

Here, the number of the observations is 7.

Let L is the largest value and S is the smallest value of the variable, then

The range of the data = $L - S......(1)$

In this case, the largest (L) value = 10 and the smallest value(S) = 2.

Now put the value of L = 10 and S = 2 in the equation (1), we get
The range of the data = 10-2 = 8.

The coefficient of the range is defined as
Coefficient of the range = $\dfrac{{L - S}}{{L + S}}.........(2)$

Now put the value of L = 10 and S = 2 in the equation (2), we get
Coefficient of the range = $\dfrac{{10 - 2}}{{10 + 2}}$
Coefficient of the range =$\dfrac{8}{{12}}$
Coefficient of the range =$\dfrac{2}{3}$

Hence, the correct option of the given question is option (a).

Note: Range is based on two extreme observations. It gives no weight to the central values of the data (Range of the data = $L - S$). It is a poor measure of dispersion and does not give a good picture of the overall spread of the observations with respect to the center of the observations.