Question

question 5
find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already sorted. the number of data is n = 8.
do not round your answers.
x
10
11
16
17
21
24
26
30
median =
q1 =
q3 =

Explanation:

Step1: Calculate median position

For $n = 8$ (even - numbered data set), median position is $\frac{n}{2}=4$ and $\frac{n}{2}+ 1 = 5$. Median is average of 4th and 5th ordered data values.
Median=$\frac{17 + 21}{2}$

Step2: Calculate first - quartile position

$Q_1$ position for $n = 8$ is $\frac{n+1}{4}=\frac{9}{4}=2.25$. $Q_1$ is $0.25$ of the way between 2nd and 3rd ordered data values.
$Q_1=11+(16 - 11)\times0.25=11 + 1.25 = 12.25$

Step3: Calculate third - quartile position

$Q_3$ position for $n = 8$ is $\frac{3(n + 1)}{4}=\frac{3\times9}{4}=6.75$. $Q_3$ is $0.75$ of the way between 6th and 7th ordered data values.
$Q_3=24+(26 - 24)\times0.75=24 + 1.5 = 25.5$

Answer:

Median: $19$
$Q_1$: $12.25$
$Q_3$: $25.5$