chapter 2 homework assignment\nscore: 23/76 answered: 5/12\nquestion 6\n1.46/47 means, medians, standard…

Explanation:

Step1: Arrange Dataset I in order

The dataset I is already in order: 3, 5, 6, 7, 9.

Step2: Find the median of Dataset I

For a dataset with $n = 5$ (odd - numbered), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{5+1}{2}=3$, so the median is 6.

Step3: Find quartiles of Dataset I

The lower half is 3, 5. The first - quartile $Q_1$ is the median of the lower half, so $Q_1=\frac{3 + 5}{2}=4$. The upper half is 7, 9. The third - quartile $Q_3$ is the median of the upper half, so $Q_3=\frac{7+9}{2}=8$. The IQR of Dataset I is from 4 to 8.

Step4: Calculate the mean of Dataset I

The mean $\bar{x}=\frac{3 + 5+6+7+9}{5}=\frac{30}{5}=6$.

Step5: Calculate the standard deviation of Dataset I

First, find the deviations from the mean: $(3 - 6)^2=9$, $(5 - 6)^2 = 1$, $(6 - 6)^2=0$, $(7 - 6)^2=1$, $(9 - 6)^2 = 9$. The variance $s^2=\frac{9+1+0+1+9}{5}=\frac{20}{5}=4$. The standard deviation $s=\sqrt{4}=2$.

Step6: Arrange Dataset II in order

Arrange Dataset II: 3, 5, 7, 8, 9.

Step7: Find the median of Dataset II

For $n = 5$ (odd - numbered), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{5 + 1}{2}=3$, so the median is 7.

Step8: Find quartiles of Dataset II

The lower half is 3, 5. The first - quartile $Q_1=\frac{3+5}{2}=4$. The upper half is 8, 9. The third - quartile $Q_3=\frac{8 + 9}{2}=8.5$. The IQR of Dataset II is from 4 to 8.5.

Step9: Calculate the mean of Dataset II

The mean $\bar{x}=\frac{3+5+8+7+9}{5}=\frac{32}{5}=6.4$.

Answer:

a) 6 b) 4, 8 c) 6 d) 2 e) 7 f) 4, 8.5 g) 6.4