$$ \{1,28,2,24,13,15,30,8,9,25,5,27\} $$ Which hox plot represents the data?

Question

UpStudy AI · Accepted Answer

1. **Sort the Data**

Given data set:  
   $$
   \{1,28,2,24,13,15,30,8,9,25,5,27\}
   $$
   
   Sorted in ascending order:  
   $$
   1,\,2,\,5,\,8,\,9,\,13,\,15,\,24,\,25,\,27,\,28,\,30
   $$
   
2. **Determine the Minimum and Maximum**

- Minimum: $$1$$
   - Maximum: $$30$$

3. **Find the Median $$M$$**

The total number of data points is $$12$$ (an even number).  
   The median is the average of the 6th and 7th values.
   
   $$
   M = \frac{13 + 15}{2} = 14
   $$

4. **Calculate the Lower Quartile $$Q_1$$**

Lower half (first 6 numbers):  
   $$
   1,\,2,\,5,\,8,\,9,\,13
   $$
   
   Median of the lower half is the average of the 3rd and 4th values:
   
   $$
   Q_1 = \frac{5 + 8}{2} = 6.5
   $$

5. **Calculate the Upper Quartile $$Q_3$$**

Upper half (last 6 numbers):  
   $$
   15,\,24,\,25,\,27,\,28,\,30
   $$
   
   Median of the upper half is the average of the 3rd and 4th values:
   
   $$
   Q_3 = \frac{25 + 27}{2} = 26
   $$

6. **Summary for the Box Plot**

- Minimum: $$1$$
   - Lower Quartile ($$Q_1$$): $$6.5$$
   - Median: $$14$$
   - Upper Quartile ($$Q_3$$): $$26$$
   - Maximum: $$30$$

7. **Representation of the Box Plot**

The box plot will have:
   
   - A box ranging from $$Q_1 = 6.5$$ to $$Q_3 = 26$$
   - A line inside the box at the median $$14$$
   - Whiskers extending from the minimum $$1$$ to the maximum $$30$$

Thus, the box plot representing the data is defined by:
   
$$
\text{Min} = 1,\quad Q_1 = 6.5,\quad \text{Median} = 14,\quad Q_3 = 26,\quad \text{Max} = 30
$$
The box plot for the data has: - Minimum: 1 - Lower Quartile (Q₁): 6.5 - Median: 14 - Upper Quartile (Q₃): 26 - Maximum: 30

Which hox plot represents the data?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Statistics Questions