Answer:
To make a box-and-whisker plot, we first need to order the data from smallest to largest:
4, 5, 6, 10, 15, 16, 21
Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.
Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:
4, 5, 6, 10 and 15, 16, 21
The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.
Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:
Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)
Plugging in the values, we get:
Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25
Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.
Therefore, the box-and-whisker plot for the given data is:
| 4
___|___
| |
| |
| 5.5 |-----
| | |
| | |
|------------| 10 |
| | |
| 15.5 |------
| | |
___|___
| 21
The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.
Hope this helps!