Make a box-and-whisker plot of the data.
21, 21, 22, 20, 13, 13, 27, 24
Box-and-whisker plot:
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|----|
| |13| |20| |21| |22| |24| |27| |
|____|
To make a box-and-whisker plot of the data, follow these steps:
1. Arrange the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
2. Find the minimum value (the smallest data point):
The minimum value is 13.
3. Find the maximum value (the largest data point):
The maximum value is 27.
4. Find the median (the middle value) of the dataset:
Since there are 8 data points, the median is the average of the two middle values, which are 21 and 22.
Median = (21 + 22) / 2 = 43 / 2 = 21.5
5. Find the lower quartile (Q1), which is the median of the lower half of the dataset:
There are 4 data points in the lower half of the dataset, and the middle two values are 13 and 20.
Lower Quartile (Q1) = (13 + 20) / 2 = 33 / 2 = 16.5
6. Find the upper quartile (Q3), which is the median of the upper half of the dataset:
There are 4 data points in the upper half of the dataset, and the middle two values are 21 and 24.
Upper Quartile (Q3) = (21 + 24) / 2 = 45 / 2 = 22.5
7. Calculate the interquartile range (IQR), which is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 22.5 - 16.5 = 6
Now, let's draw the box-and-whisker plot using these values:
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---|-13---20---21.5---22.5---24---|---
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The box represents the range from Q1 (lower quartile) to Q3 (upper quartile).
The line in the middle of the box represents the median.
The lines outside the box (whiskers) represent the minimum and maximum values.
In this plot, the minimum value is 13, the lower quartile (Q1) is 16.5, the median is 21.5, the upper quartile (Q3) is 22.5, and the maximum value is 27.
To create a box-and-whisker plot for the given data:
Step 1: Sort the data in ascending order:
13, 13, 20, 21, 21, 22, 24, 27
Step 2: Find the minimum and maximum values in the dataset:
Minimum value: 13
Maximum value: 27
Step 3: Calculate the median (middle value):
Median = (21 + 22) / 2 = 21.5
Step 4: Determine the lower quartile (Q1):
Lower quartile (Q1) = median of the lower values
Q1 = (13 + 20) / 2 = 16.5
Step 5: Determine the upper quartile (Q3):
Upper quartile (Q3) = median of the upper values
Q3 = (22 + 24) / 2 = 23
Step 6: Determine any outliers in the dataset:
No data points are considered outliers in this case.
Step 7: Represent the data in a box-and-whisker plot:
Minimum | Q1 | Median | Q3 | Maximum
13 16.5 21.5 23 27
The box portion of the plot spans from Q1 to Q3, with the median represented by a line within the box. The whiskers extend to the minimum and maximum values.