7. DIG DEEPER? Tornadoes in Region A travel significantly farther than tornadoes in Region B. The tornadoes in Region A travel a median of 10 miles. Create a double box-and-whisker plot that can represent the distances traveled by the tornadoes in the two regions.

Question

UpStudy AI · Accepted Answer

$$
\textbf{Step 1. Five-Number Summaries}
$$

A double box‐and‐whisker plot displays the minimum, first quartile ($$Q_1$$), median, third quartile ($$Q_3$$), and maximum for each data set. Here we know that for Region A the median is given as $$10$$ miles and, based on the description “tornadoes in Region A travel significantly farther than tornadoes in Region B,” we choose numbers that reflect a rightward shift in Region A’s data compared to Region B.

We can choose the following example values:

- $$\textbf{Region A:}$$ 
  - Minimum: $$4$$ miles
  - First Quartile: $$8$$ miles
  - Median: $$10$$ miles
  - Third Quartile: $$14$$ miles
  - Maximum: $$22$$ miles

- $$\textbf{Region B:}$$
  - Minimum: $$1$$ mile
  - First Quartile: $$3$$ miles
  - Median: $$5$$ miles
  - Third Quartile: $$7$$ miles
  - Maximum: $$9$$ miles

$$
\textbf{Step 2. Constructing the Number Line}
$$

To represent both regions on the same scale, we need a number line that covers the range from the lowest minimum to the highest maximum. In our example, the scale might run from $$0$$ to $$25$$ miles.

$$
\textbf{Step 3. Sketching the Box-and-Whisker Plots}
$$

Below is an example of how the two plots might be drawn on the same horizontal number line. (Note that this sketch uses a monospaced font to align the elements.)

```
Number line:  0         5         10        15        20        25
              |---------|---------|---------|---------|---------|
Region B   :        *----[3]----|----[5]----|----[7]----*       
              (min=1)         (median=5)           (max=9)
              
Region A   :              *---[8]----|----[10]---|----[14]---*   
              (min=4)         (median=10)           (max=22)
```

$$
\textbf{Explanation of the Sketch:}
$$

- For each region, the ends with a star ($$*$$) represent the minimum and maximum.
- The brackets $$[\ ]$$ show the first quartile ($$Q_1$$), median, and third quartile ($$Q_3$$).
- Region B’s box (from $$Q_1=3$$ to $$Q_3=7$$) is shifted to the left compared to Region A’s box (from $$Q_1=8$$ to $$Q_3=14$$).
- The median for Region A is $$10$$ miles, as given.

$$
\textbf{Step 4. Final Observation}
$$

This double box‐and‐whisker plot clearly demonstrates that tornadoes in Region A tend to travel farther than those in Region B. The entire distribution of Region A is shifted to larger distances, with a higher median and higher maximum value.

$$
\textbf{Conclusion:}
$$

The diagram above is a valid double box‐and‐whisker plot representing the data for the two regions. Keep in mind that the chosen numbers (except the given median for Region A) are an example; other five-number summaries with the same relative positions can also represent the situation described.
Here is a double box-and-whisker plot showing that tornadoes in Region A travel farther than those in Region B. Region A has a median of 10 miles, while Region B has a median of 5 miles.

7. DIG DEEPER? Tornadoes in Region A travel significantly farther than tornadoes in Region B. The tornadoes in Region A travel a median of 10 miles. Create a double box-and-whisker plot that can represent the distances traveled by the tornadoes in the two regions.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Statistics Questions