Question

Find the range of the following data set. 1 1/4, 5/8, 3/4, 1/2, 1 1/2, 1 3/4

A) 1
B) 1 1/8
C) 1 1/4

Answer 1

The answer is C. 1 1/4

Explanation:

To get the range of a set of data, all you need to do is get the difference between the highest value and the lowest value. Since you have different fractions, you first need to determine which is the highest and the lowest.

Since your given are not similar fractions (they do not have the same denominator), you need to make them similar first.

What I did first is make all mixed fractions into improper to make it easier for me to make them similar.

`1(1)/(4),(5)/(8),(3)/(4),(1)/(2),1(1)/(2),1(3)/(4)\\\\\\(5)/(4),(5)/(8),(3)/(4),(1)/(2),(3)/(2),(7)/(4)`

The LCD of all fractions is 8 so I will need to get the proper proportion that will make all of them have 8 as the denominator.

`(5)/(4)*(2)/(2)` ,
`(5)/(8)*(1)/(1)` ,
`(3)/(4)*(2)/(2)` ,
`(1)/(2)*(4)/(4)` ,
`(3)/(2)*(4)/(4)` ,
`(7)/(4)*(2)/(2)`

So now we have the new set of fractions to compare:

`(10)/(8), (5)/(8),(6)/(8), (4)/(8), (12)/(8),(14)/(8)`

Looking at the set, all you have to do is get the fraction with the highest numerator (which will be our highest value) and get the fraction with the lowest numerator (which is the lowest value), then get the difference.

`(14)/(8)-(4)/(8) = (10)/(8)` or
`1(2)/(8)`

Simplify it and you will get:

`1(1)/(4)`

Answer 2

Option C is correct

Explanation:

First we will convert the mixed fractions into fraction form.

5/4, 5/8, 3/4, 1/2, 3/2, 7/4

Now, to find the range the formula used is:

Range= Maximum Value - Minimum Value

To find the maximum value and minimum value in fractions, we need to make the denominator of each fraction same. Since the highest value of denominator is 8, so other fractions denominator should be 8.

10/8, 5/8, 6/8,4/8,12/8,14/8

Maximum Value = 14/8 (having highest numerator)

Minimum value = 4/8 (having lowest numerator)

Range of data set = Maximum Value - Minimum value

= 14/8 - 4/8

= 10/8 = 5/4

= 1 1/4

so, option C is correct.