directions: solve the following problems by finding the median, interquartile range (iqr), or range. you may…

Explanation:

Step1: Sort the data set {13, 15, 9, 35, 25}

{9, 13, 15, 25, 35}

Step2: Find the median

Since there are 5 data - points (n = 5), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{5+1}{2}=3$ - rd value, so Median = 15.

Step3: Find Q1 and Q3

The lower half of the data set is {9, 13}, and the upper half is {25, 35}. For the lower half (n = 2), the median of the lower half (Q1) is $\frac{9 + 13}{2}=11$. For the upper half (n = 2), the median of the upper half (Q3) is $\frac{25+35}{2}=30$.

Step4: Calculate the IQR

IQR=Q3 - Q1, so IQR = 30 - 11=19.

Step5: Sort the data set {6, 1, 3, 8, 5, 11, 1, 5}

{1, 1, 3, 5, 5, 6, 8, 11}

Step6: Find the median

Since there are 8 data - points (n = 8), the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th values. $\frac{8}{2}=4$ and $\frac{8}{2}+1 = 5$. Median=$\frac{5 + 5}{2}=5$.

Step7: Find Q1 and Q3

The lower half of the data set is {1, 1, 3, 5}, and the upper half is {5, 6, 8, 11}. For the lower half (n = 4), the median of the lower half (Q1) is $\frac{1+3}{2}=2$. For the upper half (n = 4), the median of the upper half (Q3) is $\frac{6 + 8}{2}=7$.

Step8: Calculate the IQR

IQR=Q3 - Q1, so IQR = 7 - 2=5.

Answer:

1. Median = 15 Q1 = 11 Q3 = 30 IQR = 19
2. Median = 5 Q1 = 2 Q3 = 7 IQR = 5