Finite Math Examples
22 , 44 , 66 , 88 , 1010 , 1212 , 1414 , 1616
Step 1
There are 88 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
Step 2
Arrange the terms in ascending order.
2,4,6,8,10,12,14,162,4,6,8,10,12,14,16
Step 3
Step 3.1
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.
8+1028+102
Step 3.2
Remove parentheses.
8+1028+102
Step 3.3
Cancel the common factor of 8+108+10 and 22.
Step 3.3.1
Factor 22 out of 88.
2⋅4+1022⋅4+102
Step 3.3.2
Factor 22 out of 1010.
2⋅4+2⋅522⋅4+2⋅52
Step 3.3.3
Factor 22 out of 2⋅4+2⋅52⋅4+2⋅5.
2⋅(4+5)22⋅(4+5)2
Step 3.3.4
Cancel the common factors.
Step 3.3.4.1
Factor 22 out of 22.
2⋅(4+5)2(1)2⋅(4+5)2(1)
Step 3.3.4.2
Cancel the common factor.
2⋅(4+5)2⋅1
Step 3.3.4.3
Rewrite the expression.
4+51
Step 3.3.4.4
Divide 4+5 by 1.
4+5
4+5
4+5
Step 3.4
Add 4 and 5.
9
Step 3.5
Convert the median 9 to decimal.
9
9
Step 4
The upper half of data is the set above the median.
10,12,14,16
Step 5
Step 5.1
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.
12+142
Step 5.2
Remove parentheses.
12+142
Step 5.3
Cancel the common factor of 12+14 and 2.
Step 5.3.1
Factor 2 out of 12.
2⋅6+142
Step 5.3.2
Factor 2 out of 14.
2⋅6+2⋅72
Step 5.3.3
Factor 2 out of 2⋅6+2⋅7.
2⋅(6+7)2
Step 5.3.4
Cancel the common factors.
Step 5.3.4.1
Factor 2 out of 2.
2⋅(6+7)2(1)
Step 5.3.4.2
Cancel the common factor.
2⋅(6+7)2⋅1
Step 5.3.4.3
Rewrite the expression.
6+71
Step 5.3.4.4
Divide 6+7 by 1.
6+7
6+7
6+7
Step 5.4
Add 6 and 7.
13
Step 5.5
Convert the median 13 to decimal.
13
13