Question

5 from unit 1, lesson 9
a. what is the five - number summary for the data?
0 2 2 4 5 5 5 7 11
b. when the minimum, 0, is removed from the data set, what is the five - number summary?
6 from unit 1, lesson 9
what effect does eliminating the highest value, 180, from the data set have on the mean and median?
25 50 50 60 70 85 85 90 90 180
7 from unit 1, lesson 3
the histogram represents the distribution of the number of seconds it took for each of 50 students to find the answer to a trivia question using the internet. which interval contains the median?
a. 0 to 5 seconds
b. 5 to 10 seconds
c. 10 to 15 seconds
d. 15 to 20 seconds

Explanation:

5a

Step1: Sort the data

$0,2,2,4,5,5,5,7,11$

Step2: Find minimum

The minimum is $0$.

Step3: Find first - quartile ($Q_1$)

There are $n = 9$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=2.5$. So, $Q_1=\frac{2 + 2}{2}=2$.

Step4: Find median ($Q_2$)

The position of the median is $\frac{n+1}{2}=5$, so the median is $5$.

Step5: Find third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=7.5$. So, $Q_3=\frac{5+7}{2}=6$.

Step6: Find maximum

The maximum is $11$.

Step1: Remove 0 from data

The new data set is $2,2,4,5,5,5,7,11$.

Step2: Find minimum

The minimum is $2$.

Step3: Find first - quartile ($Q_1$)

There are $n = 8$ data points. The position of $Q_1$ is $\frac{n}{4}=2$. So, $Q_1 = 2$.

Step4: Find median ($Q_2$)

The position of the median is $\frac{n}{2}=4$. The median is $\frac{5 + 5}{2}=5$.

Step5: Find third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3n}{4}=6$. So, $Q_3 = 5$.

Step6: Find maximum

The maximum is $11$.

Step1: Calculate original mean

The original data set is $25,50,50,60,70,85,85,90,90,180$. The sum is $25+50+50+60+70+85+85+90+90+180 = 785$. The mean is $\frac{785}{10}=78.5$. The median: Since $n = 10$, the median is $\frac{70 + 85}{2}=77.5$.

Step2: Calculate new mean

Remove $180$. The new sum is $785-180 = 605$. The new mean is $\frac{605}{9}\approx67.22$.

Step3: Calculate new median

The new data set has $n = 9$ data points. The median is the 5 - th value, which is $70$.

Step4: Analyze changes

The mean decreases from $78.5$ to approximately $67.22$. The median decreases from $77.5$ to $70$.

Answer:

Minimum: $0$, $Q_1:2$, Median: $5$, $Q_3:6$, Maximum: $11$

5b