Create a box-and-whisker plot for the data 10, 8, 9,16, 19, 15, 20, 16, 21, 22, 19
To create a box-and-whisker plot for the given data, we first need to determine the five-number summary:
The minimum is 8.
The first quartile (Q1) is the middle value between the minimum and the median, which is (8+15)/2 = 11.5.
The median (Q2) is the middle value of the dataset, which is 16.
The third quartile (Q3) is the middle value between the median and the maximum, which is (19+22)/2 = 20.5.
The maximum is 22.
Now, we can draw the box-and-whisker plot:
5% 25% 50% 75% 95%
___ ___ ___ ___ ___
| | | | |
8 ------| | | | |
| | | | |
9.25 11.5 16 20.5 21.75
|_____________|______|________|
The box portion of the plot represents the middle 50% of the data, with the bottom edge representing the first quartile (Q1) at 11.5 and the top edge representing the third quartile (Q3) at 20.5. The line inside the box represents the median (Q2) at 16.
The whiskers represent the smallest and largest data points that are not considered outliers. These are found by calculating 1.5 times the interquartile range (IQR = Q3 - Q1) and adding/subtracting it from Q1/Q3. Any point beyond these whiskers is considered an outlier and is represented as a separate point. In this case, we do not have any outliers.
The plot shows that the data is skewed to the right, with a longer tail on the right side of the box. The middle 50% of the data falls between 11.5 and 20.5, with the median at 16. The range of the data is from 8 to 22.