Make a box-and-whisker plot for the set of data.
21, 27, 27, 25, 21, 13, 18, 25
To create a box-and-whisker plot, first, you need to find the five key statistical values: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum.
1. Order the data set from lowest to highest:
13, 18, 21, 21, 25, 25, 27, 27
2. Find the median (Q2): Since there are 8 values, the median will be the average of the two middle values (21 and 21).
Median (Q2) = (21 + 21) / 2 = 21
3. Find the lower quartile (Q1): This is the median of the lower half of the data. In this case, it's the median of 13, 18, 21, and 21.
Lower Quartile (Q1) = (18 + 21) / 2 = 19.5
4. Find the upper quartile (Q3): This is the median of the upper half of the data. In this case, it's the median of 25, 25, 27, and 27.
Upper Quartile (Q3) = (25 + 25) / 2 = 25
5. Identify the minimum (13) and maximum (27) values.
Now you can create the box-and-whisker plot:
1. Draw a number line representing the range of data.
2. Place a vertical line at each of the five key statistical values (13, 19.5, 21, 25, 27).
3. Draw a box connecting the lower quartile (19.5) to the upper quartile (25), and draw a vertical line inside the box at the median (21).
4. Extend whiskers (horizontal lines) from the box to the minimum (13) and maximum (27).
Here's a rough sketch of the box-and-whisker plot:
----|-|-|---|-|---
13 19.5 21 25 27
It should be vertical when it's properly drawn.
To create a box-and-whisker plot, you need to arrange the data in ascending order first:
13, 18, 21, 21, 25, 25, 27, 27
Now, let's find the five-number summary:
1. Minimum: The smallest value in the data set is 13.
2. Lower Quartile (Q1): To find the lower quartile, find the median of the lower half of the data. In this case, the lower half is 13, 18, 21, 21. The median of this set is (18 + 21) / 2 = 19.5. So, Q1 = 19.5.
3. Median (Q2): The median is the value that splits the data set into two equal halves. In this case, since there are an even number of values, the median is the average of the two middle values, which are 21 and 25. So, Q2 = (21 + 25) / 2 = 23.
4. Upper Quartile (Q3): To find the upper quartile, find the median of the upper half of the data. In this case, the upper half is 25, 25, 27, 27. The median of this set is (25 + 27) / 2 = 26. So, Q3 = 26.
5. Maximum: The largest value in the data set is 27.
Now, we can create the box-and-whisker plot. Draw a number line and mark the values 13, 18, 19.5, 21, 23, 25, 26, 27.
- Draw a box from the lower quartile (Q1 = 19.5) to the upper quartile (Q3 = 26).
- Draw a vertical line inside the box at the median (Q2 = 23).
- Extend lines (whiskers) from the ends of the box to the minimum (13) and maximum (27) values.
Your completed box-and-whisker plot should look like this:
10 20 30
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13 26
I hope this helps! Let me know if you have any further questions.
To make a box-and-whisker plot for the given set of data, follow these steps:
Step 1: Arrange the data in ascending order: 13, 18, 21, 21, 25, 25, 27, 27.
Step 2: Find the median of the data set. In this case, we have 8 data points, so the median is the average of the 4th and 5th values, which are both 25.
Step 3: Find the lower quartile (Q1), which is the median of the lower half of the data set. The lower half of the data set is 13, 18, 21, and 21. Again, we have 4 data points, so the median is the average of the 2nd and 3rd values, which are both 19.5.
Step 4: Find the upper quartile (Q3), which is the median of the upper half of the data set. The upper half of the data set is 25, 25, 27, and 27. Similarly, the median is the average of the 2nd and 3rd values, which are both 26.
Step 5: Find the interquartile range (IQR) by subtracting Q1 from Q3. In this case, IQR = 26 - 19.5 = 6.5.
Step 6: Determine the minimum and maximum values in the data set. The minimum value is 13, and the maximum value is 27.
Step 7: Construct the box-and-whisker plot using the values found in the previous steps.
27 27
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| 25 25
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21 21 18 13
In the plot, the median is represented by a line segment within the box. The box represents the interquartile range, with Q1 and Q3 marking the ends of the box. The line segments extending from the box (whiskers) represent the minimum and maximum values.