Make a box-and-whisker plot of the data. 60,63,53,66,65,58,51,55,58,51,58,62,53,66,61,51,65,52,54,50
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B
D
C
D
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Do the lowest next lowest median next high and next highest
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To make a box-and-whisker plot of the given data, follow these steps:
1. Start by ordering the data values in ascending order:
50, 51, 51, 51, 52, 53, 53, 54, 55, 58, 58, 58, 60, 61, 62, 63, 65, 65, 66, 66
2. Find the median (middle value) of the data set. In this case, the median is the average of the two middle values since there are an even number of data points. The middle values are 58 and 60, so their average is 59.
3. Determine the lower quartile (Q1), which is the median of the lower half of the data. In this case, the lower half is 50, 51, 51, 51, 52, 53, 53, 54, 55, and 58. The median of this set is 52.
4. Similarly, find the upper quartile (Q3), which is the median of the upper half of the data. In this case, the upper half is 60, 61, 62, 63, 65, 65, 66, and 66. The median of this set is 64.
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: IQR = Q3 - Q1 = 64 - 52 = 12.
6. Draw a number line or a horizontal axis and plot the following points:
- The lower extreme, which is the smallest data value (50).
- The lower quartile (Q1) at a distance of IQR / 4 (12 / 4 = 3 units) above the lower extreme.
- The median (Q2) at a distance of 2 * (IQR / 4) (2 * 3 = 6 units) above Q1.
- The upper quartile (Q3) at a distance of 3 * (IQR / 4) (3 * 3 = 9 units) above Q1.
- The upper extreme, which is the largest data value (66).
7. Finally, draw a box connecting the lower and upper quartiles (Q1 and Q3), and draw vertical lines (whiskers) extending from the box to the lower and upper extremes.
The completed box-and-whisker plot for the given data would look like this:
```
50 52 58 64 66
|---------------------------------|---------------------------|
```
I hope the explanation was helpful! If you have any more questions, feel free to ask.