12. A group of 20 students, each from different schools, competed in an interschool diving competition. They each performed one dive and received a score from 1 to 100 . $$ \begin{array}{llllllllllllllllllll}62 & 100 & 39 & 50 & 93 & 25 & 53 & 53 & 44 & 43 & 40 & 28 & 36 & 30 & 84 & 84 & 59 & 100 & 58 & 76\end{array} $$ a. Use a calculator to construct a boxplot from the data. b. The percentage of students that received a score of more than 80 is closest to A. $$ 25 \% $$ B. $$ 50 \% $$ C. $$ 75 \% $$ D. $$ 100 \% $$ c. The percentage of students that received a score between 39.5 and 80 is closest to A. $$ 25 \% $$ B. $$ 50 \% $$ C. $$ 75 \% $$ D. $$ 100 \% $$

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1. **Sort the data.**

The 20 scores are:  
   $$62,\ 100,\ 39,\ 50,\ 93,\ 25,\ 53,\ 53,\ 44,\ 43,\ 40,\ 28,\ 36,\ 30,\ 84,\ 84,\ 59,\ 100,\ 58,\ 76$$.

When ordered from smallest to largest, the data become:  
   $$25,\ 28,\ 30,\ 36,\ 39,\ 40,\ 43,\ 44,\ 50,\ 53,\ 53,\ 58,\ 59,\ 62,\ 76,\ 84,\ 84,\ 93,\ 100,\ 100$$.

2. **Construct the boxplot.**

- **Minimum:** $$25$$
   - **Maximum:** $$100$$
   - **Median:**  
     
     Since there are 20 data points, the median is the average of the 10th and 11th values. Both the 10th and 11th values are $$53$$, so:  
     $$
     \text{Median} = \frac{53+53}{2} = 53.
     $$
     
   - **Lower Quartile ($$Q_1$$):**  
     
     Consider the lower 10 scores:  
     $$25,\ 28,\ 30,\ 36,\ 39,\ 40,\ 43,\ 44,\ 50,\ 53$$.  
     The median of these 10 values is the average of the 5th and 6th values:  
     $$
     Q_1 = \frac{39+40}{2} = 39.5.
     $$
     
   - **Upper Quartile ($$Q_3$$):**  
     
     Consider the upper 10 scores:  
     $$53,\ 58,\ 59,\ 62,\ 76,\ 84,\ 84,\ 93,\ 100,\ 100$$.  
     The median of these 10 values is the average of the 5th and 6th values:  
     $$
     Q_3 = \frac{76+84}{2} = 80.
     $$
     
   The five-number summary is:  
   $$
   \text{Minimum} = 25,\ Q_1 = 39.5,\ \text{Median} = 53,\ Q_3 = 80,\ \text{Maximum} = 100.
   $$

3. **Answering part (b).**

We need the percentage of students that received a score of more than $$80$$.

- Identify scores $$> 80$$ from our sorted data:  
     $$84,\ 84,\ 93,\ 100,\ 100$$.  
     
   - There are $$5$$ scores out of $$20$$.

- Thus, the percentage is:  
     $$
     \frac{5}{20} \times 100\% = 25\%.
     $$

The answer is **$$25\%$$** (Choice A).

4. **Answering part (c).**

We need the percentage of students that received a score between $$39.5$$ and $$80$$.

- Identify scores between $$39.5$$ and $$80$$ (inclusive):  
     
     From the ordered list, these scores are:  
     $$40,\ 43,\ 44,\ 50,\ 53,\ 53,\ 58,\ 59,\ 62,\ 76$$.

- There are $$10$$ scores out of $$20$$.

- Thus, the percentage is:  
     $$
     \frac{10}{20} \times 100\% = 50\%.
     $$

The answer is **$$50\%$$** (Choice B).
- **Boxplot:** - **Minimum:** 25 - **First Quartile (Q₁):** 39.5 - **Median:** 53 - **Third Quartile (Q₃):** 80 - **Maximum:** 100 - **Part (b):** - **Percentage of students with scores > 80:** 25% (Choice A) - **Part (c):** - **Percentage of students with scores between 39.5 and 80:** 50% (Choice B)

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