Question

Question was provided via image upload.

Explanation:

Step1: Analyze the Box - and - Whisker Plot

In a box - and - whisker plot, the box represents the inter - quartile range (IQR), with the left end of the box being the first quartile ($Q_1$), the line inside the box being the second quartile (median, $Q_2$), and the right end of the box being the third quartile ($Q_3$). The whiskers extend from the minimum value to $Q_1$ and from $Q_3$ to the maximum value.

Let's assume the number line has markings. Let's suppose the minimum value ($\text{min}$) is at some point, $Q_1$ at another, $Q_2$ (median) at the middle of the box, $Q_3$ at the right end of the box, and maximum value ($\text{max}$) at the end of the right whisker.

Step2: Recall Formulas

• The second quartile ($Q_2$) is the median of the data set. In a box - and - whisker plot, it is the line inside the box.
• The range is calculated as $\text{Range}=\text{max}-\text{min}$.
• The inter - quartile range (IQR) is calculated as $\text{IQR}=Q_3 - Q_1$.
• The third quartile ($Q_3$) is the right end of the box in the box - and - whisker plot.

However, since the exact markings on the number line are not clearly visible from the provided image, we need to assume the positions. Let's assume the number line has values (for example, if we assume the minimum is at 3, $Q_1$ at 5, $Q_2$ at 6, $Q_3$ at 7, and maximum at 9):

For part a) (2nd quartile - $Q_2$)

The 2nd quartile is the median. In the box - and - whisker plot, it's the line inside the box. If we assume the middle line of the box is at 6 (for example), then $Q_2 = 6$.

For part b) (Range)

Range = max - min. If max is 9 and min is 3, then Range=$9 - 3=6$.

For part c) (IQR)

IQR=$Q_3 - Q_1$. If $Q_3 = 7$ and $Q_1 = 5$, then IQR=$7 - 5 = 2$.

For part d) (3rd quartile - $Q_3$)

The 3rd quartile is the right end of the box. If the right end of the box is at 7 (for example), then $Q_3=7$.

(Note: Since the original image's number line markings are not clear, the above is a general approach. To get the exact answer, we need the clear markings on the number line. If we assume the number line has the following markings (from left to right): 3,4,5,6,7,8,9,10 (assuming the leftmost is 3 and rightmost is 10) and the box is from 5 to 7 with the median line at 6, and whiskers from 3 to 5 and 7 to 9):

a) 2nd quartile ($Q_2$): The median is the middle value. For a box - and - whisker plot, it's the line inside the box. So if the box is between 5 and 7 and the middle line is at 6, $Q_2 = 6$.

b) Range: Max - Min. If max is 9 and min is 3, Range = 9 - 3=6.

c) IQR: $Q_3 - Q_1$. If $Q_3 = 7$ and $Q_1 = 5$, IQR=7 - 5 = 2.

d) 3rd quartile ($Q_3$): The right end of the box. If the box ends at 7, $Q_3 = 7$.

Answer:

a) (Assuming the median line is at 6) $\boldsymbol{6}$
b) (Assuming max = 9, min = 3) $\boldsymbol{6}$
c) (Assuming $Q_3 = 7$, $Q_1 = 5$) $\boldsymbol{2}$
d) (Assuming the right end of the box is at 7) $\boldsymbol{7}$

(Note: The answers are based on assumed number line markings. For exact answers, the clear number line markings from the image are required.)