Question

The range of the data 7, 13, 6, 25, 18, 20, 16 is _____.
A) 13
B) 19
C) 20
D) 25

Answer 1

Hint: We will first observe the given data carefully. After noting it down, we will arrange the data in ascending form. After doing that, we will note down the largest and smallest value of the data. Then the difference of those gives us the required range of the data.

Complete step-by-step answer:
We have the data 7, 13, 6, 25, 18, 20, 16 given to us in the question.
We can observe that 6 is the smallest element in this data which is occurring only once. Then comes the element 7 which is also occurring only once in the data, then we gave 13 occurring only once in the data, then we have 16 occurring only once in the data, then we have 18 occurring only once in the data, then we have 20 occurring only once in the data and at last we have 25 occurring once in the data.
Rewriting the whole data in the ascending form like: 6, 7, 13, 16, 18, 20, 25.
We can see that we have the least element as 6 and the largest element as 25.
Since we know that Range is given by: Largest element – least element.
$\therefore $ Range = 25 – 6
Simplifying the RHS of the above expression, we will get:-
$\therefore $ Range = 19

$\therefore $ The correct option is (B).

Note: The students must commit to memory that: Range = Largest element – Least element.
Let us understand what the range basically tells us? What ideas does it give to anyone?
It only tells you about how much spread the data given to us is. Like in the above question, we have the idea that the highest and lowest extreme values are 19 units or 19 numbers wide (because we found that range is coming out to be 19). But, it gives no information about the location of any point.