Question
Harris went to the store to compare prices of hiking shoes.
Shoe Style A B C D E F
Price ($) 125 110 95 135 150 375
Using the 1.5 IQR rule, determine if the mean is skewed by an outlier.
Responses
A Yes, 375 is an outlier, and the mean is skewed to the right.Yes, 375 is an outlier, and the mean is skewed to the right.
B Yes, 95 is an outlier, and the mean is skewed to the left.Yes, 95 is an outlier, and the mean is skewed to the left.
C No, there are no outliers, and the mean is not skewed.No, there are no outliers, and the mean is not skewed.
D No, 375 and 95 are both outliers, so the mean is not skewed.
Shoe Style A B C D E F
Price ($) 125 110 95 135 150 375
Using the 1.5 IQR rule, determine if the mean is skewed by an outlier.
Responses
A Yes, 375 is an outlier, and the mean is skewed to the right.Yes, 375 is an outlier, and the mean is skewed to the right.
B Yes, 95 is an outlier, and the mean is skewed to the left.Yes, 95 is an outlier, and the mean is skewed to the left.
C No, there are no outliers, and the mean is not skewed.No, there are no outliers, and the mean is not skewed.
D No, 375 and 95 are both outliers, so the mean is not skewed.
Answers
Answered by
GPT-4o mini
To use the 1.5 IQR rule to determine if there are outliers, we need to follow these steps:
1. **Find the Quartiles**:
- First, we need to sort the shoe prices: 95, 110, 125, 135, 150, 375.
- The median (Q2) is the average of the middle two numbers (125 and 135), which is \( \frac{125 + 135}{2} = 130 \).
2. **Calculate Q1 and Q3**:
- Q1 (the median of the first half of the data): The first half is 95, 110, 125; thus, Q1 is 110 (the median of these three numbers).
- Q3 (the median of the second half of the data): The second half is 135, 150, 375; thus, Q3 is 150 (the median of these three numbers).
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 150 - 110 = 40.
4. **Determine the lower and upper bounds for outliers**:
- Lower bound = Q1 - 1.5 × IQR = 110 - 1.5 × 40 = 110 - 60 = 50.
- Upper bound = Q3 + 1.5 × IQR = 150 + 1.5 × 40 = 150 + 60 = 210.
5. **Identify outliers**:
- Any data point below 50 or above 210 is considered an outlier.
- Here, 375 is greater than 210, so it is an outlier.
- The price of 95 is not below 50, so it is not an outlier.
6. **Determine skewness of the mean**:
- Since there is an outlier (375), and it is higher than the upper bound, it would skew the mean to the right.
Based on this analysis, the correct response is:
**A**: Yes, 375 is an outlier, and the mean is skewed to the right.
1. **Find the Quartiles**:
- First, we need to sort the shoe prices: 95, 110, 125, 135, 150, 375.
- The median (Q2) is the average of the middle two numbers (125 and 135), which is \( \frac{125 + 135}{2} = 130 \).
2. **Calculate Q1 and Q3**:
- Q1 (the median of the first half of the data): The first half is 95, 110, 125; thus, Q1 is 110 (the median of these three numbers).
- Q3 (the median of the second half of the data): The second half is 135, 150, 375; thus, Q3 is 150 (the median of these three numbers).
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 150 - 110 = 40.
4. **Determine the lower and upper bounds for outliers**:
- Lower bound = Q1 - 1.5 × IQR = 110 - 1.5 × 40 = 110 - 60 = 50.
- Upper bound = Q3 + 1.5 × IQR = 150 + 1.5 × 40 = 150 + 60 = 210.
5. **Identify outliers**:
- Any data point below 50 or above 210 is considered an outlier.
- Here, 375 is greater than 210, so it is an outlier.
- The price of 95 is not below 50, so it is not an outlier.
6. **Determine skewness of the mean**:
- Since there is an outlier (375), and it is higher than the upper bound, it would skew the mean to the right.
Based on this analysis, the correct response is:
**A**: Yes, 375 is an outlier, and the mean is skewed to the right.