Question

What is the range of the data: 48, 65, 27, 23, 44, 41, 25, 70, 49?

Answer 1

Hint: To solve this question, we will, first of all, define what a range is in terms of the given data set and then determine the highest and the lowest data from the given set and finally use the formula of range as Range = Highest Value – Lowest Value to get the result.

Complete step by step answer:
The given data is as
\[48,65,27,33,44,41,25,70,49\]
Let us first define the range of data. The range of data is given as the difference between the lowest and the highest value. Suppose the given data is as \[\left\{ 1,2,3,7,9,2,4,3,8 \right\}\] then the maximum value of the given data as taken in the example is 9 and the smallest or the least value of the given data as taken in the example is 1. Then, the range is the difference between the highest value and the lowest value. Here, we are given the data as:
\[48,65,27,23,44,41,25,70,49\]
Observing the data given above, we see that the least value is 23 and the highest value is 70. The range is given by the highest value – the lowest value. Substituting the highest and the lowest value, we get,
\[\text{Range of the given data}=70-23=47\]
Hence, the range of the given data set is 47.

Note: Suppose a data set is given as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then the highest value is 10 (rightmost value) and the lowest value is 1 (leftmost value). But if the data set is given as 1, 7, 8, 2, 3, 6, 10, 9, 4, 5, then we first need to make the given terms ascending and then choose the rightmost value as the highest value and left most value as the lowest value. This is another approach we can use to solve the above question.