Which is the correct box-and-whisker plot for the data set?
21, 15, 10, 16, 11, 19
No box-and-whisker sets shown.
To create a box-and-whisker plot for a given data set, you need to follow these steps:
1. Arrange the data in ascending order: 10, 11, 15, 16, 19, 21.
2. Find the minimum value, which is the smallest number in the data set. In this case, the minimum value is 10.
3. Find the maximum value, which is the largest number in the data set. In this case, the maximum value is 21.
4. Calculate the median, which is the middle value of the data set. Since the number of data points is even (6 in this case), the median is the average of the two middle values. So, (15 + 16) ÷ 2 = 15.5.
5. Calculate the lower quartile (Q1), which is the median of the lower half of the data set. In this case, the lower half is {10, 11, 15}. So, the median of the lower half is 11.
6. Calculate the upper quartile (Q3), which is the median of the upper half of the data set. In this case, the upper half is {16, 19, 21}. So, the median of the upper half is 19.
Now, let's create the box-and-whisker plot based on the above calculations:
|
21|
---------- <-- maximum
19|
16|
15|
----------- <-- median
11|
10| <-- minimum
|
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The above plot represents the given data set with the correct box-and-whisker plot.