Hallux abducto valgus (HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 19 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. The data for HAV angle are given below: 32 25 21 22 20 18 26 16 30 30 20 50 25 26 28 31 38 32 21 (a) Construct a stem and leaf plot for the data. (b) Determine the quartiles Q1, Q2 , Q3. (c) Does the data contain any outliers? Compute the inner fences, and outer fences and identify mild and extreme outliers, if any. Draw a box plot (indicating outliers, if any).
Hallux abducto valgus (HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 19 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. The data for HAV angle are given below: 32 25 21 22 20 18 26 16 30 30 20 50 25 26 28 31 38 32 21 (a) Construct a stem and leaf plot for the data. (b) Determine the quartiles Q1, Q2 , Q3. (c) Does the data contain any outliers? Compute the inner fences, and outer fences and identify mild and extreme outliers, if any. Draw a box plot (indicating outliers, if any).
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
Transcribed Image Text:**Topic: Hallux Abducto Valgus (HAV) Deformity Analysis**
Hallux abducto valgus (HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 19 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. The data for HAV angle are given below:
32, 25, 21, 22, 20, 18, 26, 16, 30, 30, 20, 50, 25, 26, 28, 31, 38, 32, 21
**(a) Construct a stem and leaf plot for the data.**
To create a stem and leaf plot, separate each data point into a stem (the leading digit or digits) and a leaf (the last digit). For example, for the number 32, the stem is 3 and the leaf is 2.
**Stem and Leaf Plot:**
```
1 | 6 8
2 | 0 0 1 1 2 5 5 6 6 8
3 | 0 0 1 2 2
4 |
5 | 0
```
**(b) Determine the quartiles Q1, Q2, Q3.**
1. **Arrange the data in ascending order:**
16, 18, 20, 20, 21, 21, 22, 25, 25, 26, 26, 28, 30, 30, 31, 32, 32, 38, 50
2. **Find Q1, Q2, Q3 (1st quartile, median, 3rd quartile):**
- **Q1 (25th percentile):** 21
- **Q2 (Median):** 26
- **Q3 (75th percentile):** 30
**(c) Does the data contain any outliers?**
Compute the inner fences and outer fences and identify mild and extreme outliers if any. Use a box plot to indicate outliers.
1. **Interquartile Range (IQR) = Q3 - Q1 =
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