# Find the Upper or Third Quartile 21 , 38 , 35 , 31 , 28 , 22 , 25 , 32 , 24 , 35 , 27 , 30

21 , 38 , 35 , 31 , 28 , 22 , 25 , 32 , 24 , 35 , 27 , 30
There are 12 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.
21,22,24,25,27,28,30,31,32,35,35,38
Find the median of 21,22,24,25,27,28,30,31,32,35,35,38.
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.
28+302
Remove parentheses.
28+302
Cancel the common factor of 28+30 and 2.
Factor 2 out of 28.
2⋅14+302
Factor 2 out of 30.
2⋅14+2⋅152
Factor 2 out of 2⋅14+2⋅15.
2⋅(14+15)2
Cancel the common factors.
Factor 2 out of 2.
2⋅(14+15)2(1)
Cancel the common factor.
2⋅(14+15)2⋅1
Rewrite the expression.
14+151
Divide 14+15 by 1.
14+15
14+15
14+15
29
Convert the median 29 to decimal.
29
29
The upper half of data is the set above the median.
30,31,32,35,35,38
The median for the upper half of data 30,31,32,35,35,38 is the upper or third quartile. In this case, the third quartile is 33.5.
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.
32+352
Remove parentheses.
32+352