# Find the Lower or First Quartile 5/4 , 1/3-1/18

54 , 13-118
There are 2 observations, so the median is the mean of the two middle numbers of the arranged set of data. Splitting the observations either side of the median gives two groups of observations. The median of the lower half of data is the lower or first quartile. The median of the upper half of data is the upper or third quartile.
The median of the lower half of data is the lower or first quartile
The median of the upper half of data is the upper or third quartile
Arrange the terms in ascending order.
13-118,54
Find the median of 13-118,54.
The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.
13-118+542
Remove parentheses.
13-118+542
Simplify the numerator.
To write 13 as a fraction with a common denominator, multiply by 66.
13⋅66-118+542
Write each expression with a common denominator of 18, by multiplying each by an appropriate factor of 1.
Multiply 13 and 66.
63⋅6-118+542
Multiply 3 by 6.
618-118+542
618-118+542
Combine the numerators over the common denominator.
6-118+542
Subtract 1 from 6.
518+542
To write 518 as a fraction with a common denominator, multiply by 22.
518⋅22+542
To write 54 as a fraction with a common denominator, multiply by 99.
518⋅22+54⋅992
Write each expression with a common denominator of 36, by multiplying each by an appropriate factor of 1.
Multiply 518 and 22.
5⋅218⋅2+54⋅992
Multiply 18 by 2.
5⋅236+54⋅992
Multiply 54 and 99.
5⋅236+5⋅94⋅92
Multiply 4 by 9.
5⋅236+5⋅9362
5⋅236+5⋅9362
Combine the numerators over the common denominator.
5⋅2+5⋅9362
Simplify the numerator.
Multiply 5 by 2.
10+5⋅9362
Multiply 5 by 9.
10+45362
Add 10 and 45.
55362
55362
55362
Multiply the numerator by the reciprocal of the denominator.
5536⋅12
Multiply 5536⋅12.
Multiply 5536 and 12.
5536⋅2
Multiply 36 by 2.
5572
5572
Convert the median 5572 to decimal.
0.7638‾
0.7638‾
The lower half of data is the set below the median.
13-118
Find the Lower or First Quartile 5/4 , 1/3-1/18

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