Question

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 1.1 2.2 3 7 11.7 14.3 16.1 19 25.3 25.9 median = q1 = q3 = question help: message instructor post to forum

Explanation:

Step1: Calculate the median position

Since $n = 10$ (even - numbered data set), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered values. $\frac{n}{2}=\frac{10}{2}=5$, $\frac{n}{2}+1 = 6$.

Step2: Find the median

Median=$\frac{11.7 + 14.3}{2}=\frac{26}{2}=13$.

Step3: Calculate the position of Q1

The first - quartile position for an even - numbered data set is at $\frac{n + 1}{4}=\frac{10+ 1}{4}=2.75$. This means Q1 is $0.75$ of the way between the 2nd and 3rd ordered values. 2nd value is $2.2$, 3rd value is $3$. Q1=$2.2+(3 - 2.2)\times0.75=2.2 + 0.6=2.8$.

Step4: Calculate the position of Q3

The third - quartile position for an even - numbered data set is at $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. This means Q3 is $0.25$ of the way between the 8th and 9th ordered values. 8th value is $19$, 9th value is $25.3$. Q3=$19+(25.3 - 19)\times0.25=19 + 1.575=20.575$.

Answer:

Median = $13$
$Q1=2.8$
$Q3 = 20.575$