make a box and whisker plot of the data
21 21 22 20
To create a box and whisker plot:
1. First, we need to find the median, the lower quartile, and the upper quartile.
2. Arrange the data in ascending order: 20, 21, 21, 22
3. Calculate the median (Q2): For this data set, there are an even number of values, so the median will be the average of the middle two values. (21+21)/2 = 21.
4. Determine the lower quartile (Q1): The lower quartile is the median of the lower half of the data. In this case, we have only two values in the lower half (20, 21), so we take the average of the two values: (20+21)/2 = 20.5
5. Determine the upper quartile (Q3): The upper quartile is the median of the upper half of the data. In this case, we have only two values in the upper half (21, 22), so we take the average of the two values: (21+22)/2 = 21.5
Now we have the information needed to create the box and whisker plot:
- The left whisker represents the minimum value, 20.
- The right whisker represents the maximum value, 22.
- The box represents the interquartile range (IQR), which extends from Q1 (20.5) to Q3 (21.5).
- The vertical line inside the box represents the median (21).
Here is the box and whisker plot for the given data:
```
├───────┬───────┤
20 20.5 21.5 22
```
Note that the box and whiskers are very close together since the data has very little spread.