Question

For the 28 EU nations, the accompanying table shows the unemployment rate among 15 - to 24 -year clids in 2013 . The unemployment rates range from 4.89 to 27.26, with Q1=7.175, median =10.14,03=13.05, a mean of 11,13 , and a standard deviation of 5.6. Complete parts a through d below. Click the icon to view the unemployment data. a. In a box plot, what would be the values at the outer edges of the box, and what would bo the values to which the whiskers extend?

Answer 1

In a box plot (also known as a box-and-whisker plot), the box represents the interquartile range (IQR), and the whiskers extend from the box to show the range of the data. Here's how you would determine the values at the outer edges of the box and the values to which the whiskers extend:

1. **Box**: The box in a box plot represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). You've already provided the values for Q1 and Q3:

- Q1 = 7.175

- Q3 = 13.05

So, the lower edge of the box corresponds to Q1, which is 7.175, and the upper edge of the box corresponds to Q3, which is 13.05.

2. **Whiskers**: The whiskers in a box plot typically extend to the minimum and maximum values within a certain range. The range is calculated as 1.5 times the IQR. To determine where the whiskers extend, you can calculate the lower and upper bounds:

- Lower bound of whisker: Q1 - (1.5 * IQR)

- Upper bound of whisker: Q3 + (1.5 * IQR)

First, calculate the IQR:

IQR = Q3 - Q1 = 13.05 - 7.175 = 5.875

Now, calculate the lower and upper bounds:

- Lower bound of whisker: 7.175 - (1.5 * 5.875) = 7.175 - 8.8125 = -1.6375 (However, it doesn't make sense to have negative values, so we consider the minimum value from the data as the lower bound)

- Upper bound of whisker: 13.05 + (1.5 * 5.875) = 13.05 + 8.8125 = 21.8625

The whisker extends from the minimum value in the data (which is 4.89) up to the upper bound, which is 21.8625.

So, in summary:

- The lower edge of the box is 7.175.

- The upper edge of the box is 13.05.

- The whisker on the left (lower side) extends to the minimum value in the data, which is 4.89.

- The whisker on the right (upper side) extends to the upper bound, which is 21.8625.

Explanation: