Question

chapter 2 homework assignment
score: 13/76 answered: 4/12
question 5
1.46/47 means, medians, standard deviations, and iqrs: answer the following about each dataset. (round to two decimal places where appropriate)
dataset i: 3 5 6 7 9
a) the median of dataset i is:
b) the iqr of dataset i is from to
c) the mean of dataset i is:
d) the standard deviation of dataset i is:
dataset ii: 3 5 6 7 20
e) the median of dataset ii is:
f) the iqr of dataset ii is from to
g) the mean of dataset ii is:

Explanation:

Step1: Find median of Dataset I

Dataset I has 5 numbers. For odd - numbered dataset, median is the middle number. So median = 6.

Step2: Find quartiles of Dataset I

First half: 3, 5. Median of first half (Q1) = 4. Second half: 7, 9. Median of second half (Q3)=8. IQR = Q3 - Q1 = 8 - 4 = 4. So IQR is from 4 to 8.

Step3: Calculate mean of Dataset I

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

Step4: Calculate standard deviation of Dataset I

$S=\sqrt{\frac{(3 - 6)^2+(5 - 6)^2+(6 - 6)^2+(7 - 6)^2+(9 - 6)^2}{5 - 1}}=\sqrt{\frac{9 + 1+0+1+9}{4}}=\sqrt{\frac{20}{4}}=\sqrt{5}\approx2.24$.

Step5: Find median of Dataset II

Dataset II has 5 numbers. Median is the middle number. So median = 6.

Step6: Find quartiles of Dataset II

First half: 3, 5. Median of first half (Q1) = 4. Second half: 7, 20. Median of second half (Q3)=$\frac{7 + 20}{2}=13.5$. IQR = Q3 - Q1 = 13.5 - 4 = 9.5. So IQR is from 4 to 13.5.

Step7: Calculate mean of Dataset II

Mean $\bar{x}=\frac{3+5+6+7+20}{5}=\frac{41}{5}=8.2$.

Answer:

a) 6
b) 4, 8
c) 6
d) 2.24
e) 6
f) 4, 13.5
g) 8.2