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

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

Add 14 and 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 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

Add 32 and 35.

672

Convert the median 672 to decimal.

33.5

33.5

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