Make a box and whisker plot of this data.
21,21,22,10,13,27,24
First, we need to find the minimum and maximum values, as well as the quartiles and median.
Minimum: 10
First Quartile (Q1): 18
Median: 21.5
Third Quartile (Q3): 24
Maximum: 27
Now we can construct the box and whisker plot:
| ___
-|----|--| |
| ---
10 18 21.5 24 27
The box represents the middle 50% of the data (from Q1 to Q3), with the median as the line inside the box. The whiskers represent the minimum and maximum values that are not outliers. Any data beyond the whiskers are considered outliers and are represented as individual points outside of the whiskers.
To create a box and whisker plot for the given data: 21, 21, 22, 10, 13, 27, 24, follow these steps:
Step 1: Arrange the data in ascending order: 10, 13, 21, 21, 22, 24, 27.
Step 2: Find the median value. Since there are 7 data points, the median will be the (7 + 1) / 2 = 4th value, which is 21.
Step 3: Find the lower quartile (Q1). Since there are 7 data points, (7 / 4) = 1.75, which means Q1 is the average of the 1st and 2nd values, which is (10 + 13) / 2 = 11.5.
Step 4: Find the upper quartile (Q3). Since there are 7 data points, (3 * 7 / 4) = 5.25, which means Q3 is the average of the 5th and 6th values, which is (22 + 24) / 2 = 23.
Step 5: Determine the minimum and maximum values in the data set. The minimum value is 10, and the maximum value is 27.
Step 6: Draw a number line that spans the range of the data set and mark the minimum, Q1, median, Q3, and maximum values on it.
Step 7: Draw a box from Q1 to Q3 on the number line.
Step 8: Draw a line segment (whisker) from the box to the minimum value (10) and another line segment from the box to the maximum value (27).
Step 9: Label your plot with the title "Box and Whisker Plot".
The completed box and whisker plot for the given data will look like this:
```
Box and Whisker Plot
____________________________
| |
10 ____| |____ 27
| |
| ----- |
| | | |
|_______21______|
Q1 Q3
```