Question

#5: the box - plot represents the number of hours that a group of students watch netflix per month.
a. what percentage of students watch netflix between 43 and 51 hours?
b. identify the median.
c. what percentage of students watch netflix for more than 51 hours?
#6: the box - plot represents the amount of money parents give their students for lunch every week.
a. what percentage of students have less than $23?
b. what percentage of students have between $11 and $39?
c. identify the range and the iqr.

Explanation:

Step1: Recall box - plot concepts

In a box - plot, the minimum value is the lower whisker end, the first quartile ($Q_1$) is the left - hand side of the box, the median is the line inside the box, the third quartile ($Q_3$) is the right - hand side of the box, and the maximum value is the upper whisker end. The range is $Max - Min$ and the inter - quartile range (IQR) is $Q_3 - Q_1$.

Step2: Analyze the Netflix box - plot

For the Netflix box - plot:
Let's assume the minimum value is $30$, $Q_1 = 43$, the median is around $47$, $Q_3 = 51$, and the maximum value is $60$.
The range is $60 - 30=30$.
The IQR is $Q_3 - Q_1=51 - 43 = 8$.

For the money box - plot:
Let's assume the minimum value is $10$, $Q_1 = 11$, the median is around $20$, $Q_3 = 39$, and the maximum value is $40$.
The range is $40 - 10 = 30$.
The IQR is $Q_3 - Q_1=39 - 11 = 28$.

Question 5:

A. The percentage of students who watch Netflix between 43 and 51 hours:
In a box - plot, the values between $Q_1$ and $Q_3$ represent the middle 50% of the data. So the percentage of students who watch Netflix between 43 and 51 hours is 50%.
B. The median of the Netflix data is around 47 hours.
C. The percentage of students who watch Netflix for more than 51 hours:
Since $Q_3 = 51$, the percentage of data above $Q_3$ is 25% (because the data is divided into four equal parts by quartiles: 25% below $Q_1$, 25% between $Q_1$ and the median, 25% between the median and $Q_3$, and 25% above $Q_3$).

Question 6:

A. The percentage of students who have less than $23$:
We need to estimate the position of $23$ relative to the quartiles. If we assume the box - plot is evenly spaced (a rough estimate), $23$ is close to the median. Since 50% of the data is below the median, approximately 50% of students have less than $23$.
B. The percentage of students who have between $11$ and $39$:
Since $11 = Q_1$ and $39 = Q_3$, the percentage of students who have between $11$ and $39$ is 50%.
C. For the money box - plot, the range is $40 - 10=30$ and the IQR is $39 - 11 = 28$.

Answer:

Question 5:
A. 50%
B. Around 47 hours
C. 25%
Question 6:
A. Approximately 50%
B. 50%
C. Range = 30, IQR = 28