Question

If the formula for the coefficient of range is defined as $\dfrac{Range}{a+b}$, then what does the terms a and b stand for?
(a) The mean and median of the data set.
(b) The maximum and the minimum value of the data set.
(c) The mean and mode value of the data set.
(d) The minimum and mean value of the data set.

Answer 1

Hint: We start solving the problem by recalling the definition of range and assigning the variables for the maximum and minimum value of the observations in the given data set. We then define the coefficient of range as the ratio of range to the sum of minimum and maximum values of the observations in the data set. We then compare this formula with the one given in the problem to get the required answer.

Complete step by step answer:
According to the problem, we are asked to define what the terms a and b are if the coefficient of range is defined as $\dfrac{Range}{a+b}$ ---(1).
Let us recall the definitions of range and the coefficient of the range.
We know that the range is defined as the difference of the maximum and minimum observation of the given data set. Let us denote the maximum and minimum observations as ${{x}_{\max }}$ and ${{x}_{\min }}$.
So, we get \[Range={{x}_{\max }}-{{x}_{\min }}\].
Similarly, we know that the coefficient of the range is defined as the ratio of range to the sum of the maximum and minimum observation of the given data set.
So, we get coefficient of Range = $\dfrac{Range}{{{x}_{\max }}+{{x}_{\min }}}$ ---(2).
Comparing equations (1) and (2), we get the terms a and b as the maximum and minimum values of the observations given in the data set.
∴ The terms a and b stand for the maximum and the minimum value of the data set.

So, the correct answer is “Option B”.

Note: We should not confuse the formulas of mean, median, mode, range and coefficient of the range before solving this problem. We can also calculate the values if any data set is mentioned in this problem. Whenever we get this type of problem, we should first recall the definitions and then compare them to get the required answers.