Question

median q3 {6,12,8,15,9,7} q1 iqr median q3 {5,9,17,25,36,45} q1 iqr

Explanation:

Step1: Sort the data sets

For $\{6,12,8,15,9,7\}$, sorted is $\{6,7,8,9,12,15\}$. For $\{5,9,17,25,36,45\}$, sorted is $\{5,9,17,25,36,45\}$.

Step2: Calculate the median for $\{6,7,8,9,12,15\}$

Since $n = 6$ (even), median=$\frac{8 + 9}{2}=8.5$. For $\{5,9,17,25,36,45\}$, median=$\frac{17+25}{2}=21$.

Step3: Find Q1 and Q3 for $\{6,7,8,9,12,15\}$

Lower half is $\{6,7,8\}$, so Q1 = 7. Upper half is $\{9,12,15\}$, so Q3 = 12. For $\{5,9,17,25,36,45\}$, lower half is $\{5,9,17\}$, Q1 = 9, upper half is $\{25,36,45\}$, Q3 = 36.

Step4: Calculate the IQR

For $\{6,7,8,9,12,15\}$, IQR=$Q3 - Q1=12 - 7 = 5$. For $\{5,9,17,25,36,45\}$, IQR=$36 - 9=27$.

Answer:

For the set $\{6,12,8,15,9,7\}$:
Median: $8.5$
Q3: $12$
Q1: $7$
IQR: $5$

For the set $\{5,9,17,25,36,45\}$:
Median: $21$
Q3: $36$
Q1: $9$
IQR: $27$