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

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: $27$

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=$36 - 9=27$.