Question

3.3 ranking: quartiles, iqr and outliers
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 = 10.
do not round your answers.
x
3.6
5.1
6.5
11.3
13.4
18.1
18.8
18.9
25.1
26.8
median =
q1 =
q3 =
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Explanation:

Step1: Calculate the median

For $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is $13.4$ and the 6th value is $18.1$. Median=$\frac{13.4 + 18.1}{2}=15.75$.

Step2: Calculate the first quartile (Q1)

The first - quartile is the median of the lower half of the data. The lower half of the data consists of the first 5 values: $3.6,5.1,6.5,11.3,13.4$. Since $n = 5$ (an odd - numbered data set), the median of this lower half (Q1) is the 3rd value, so $Q1=6.5$.

Step3: Calculate the third quartile (Q3)

The third - quartile is the median of the upper half of the data. The upper half of the data consists of the last 5 values: $18.1,18.8,18.9,25.1,26.8$. Since $n = 5$ (an odd - numbered data set), the median of this upper half (Q3) is the 3rd value, so $Q3=18.9$.

Answer:

Median = $15.75$
$Q1=6.5$
$Q3=18.9$