Make a box and whisker plot of the data.
21,21, 22,20 13 13, 27,24
A box and whisker plot is a graph that displays the median (Q2), lower quartile (Q1), upper quartile (Q3), and any outliers of a given set of data. It is used to quickly visualize the spread and skewness of the data.
Given data: 13, 13, 20, 21, 21, 22, 24, 27
1. Order the data from least to greatest
13, 13, 20, 21, 21, 22, 24, 27
2. Find the median (Q2) of the data
There are 8 data points, so we need to find the average of the 4th and 5th values.
Q2 = (21 + 21)/2 = 21
3. Find the lower quartile (Q1)
To find the lower quartile, we take the median of the lower half of the data:
Q1 = (13 + 13)/2 = 13
4. Find the upper quartile (Q3)
To find the upper quartile, we take the median of the upper half of the data:
Q3 = (22 + 24)/2 = 23
5. Identify any outliers
We would need to calculate IQR (Interquartile Range) to identify any outliers.
IQR = Q3 - Q1 = 23 - 13 = 10
Lower fence = Q1 - 1.5*IQR = 13 - 15 = -2 (any data point below this value is considered an outlier)
Upper fence = Q3 + 1.5*IQR = 23 + 15 = 38 (any data point above this value is considered an outlier)
In this case, there are no outliers.
Now, we can make a box and whisker plot using the above data:
```plaintext
---|----|-------------|------|---
13 13 21 23 27
Q1 Min Q2 Q3 Max
```
The whiskers are drawn from the minimum to Q1, and from Q3 to the maximum. The box is created from Q1 to Q3 with a vertical line in the middle, which represents the median (Q2).