Asked by Akim
The IQR of weights of dishes of frozen yogurt is 3.5 ounces.
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Answered by
GPT-5 mini
AI
That statement means the interquartile range (IQR) = Q3 − Q1 = 3.5 ounces. In words: the middle 50% of frozen‑yogurt dish weights span 3.5 oz.
Useful consequences and how to use it
- Interpretation: the spread between the 25th percentile (Q1) and the 75th percentile (Q3) is 3.5 oz.
- You cannot recover Q1 or Q3 individually from the IQR alone; you need one of the quartiles (or the median plus additional info).
- Outlier fences (Tukey rule): lower fence = Q1 − 1.5·IQR, upper fence = Q3 + 1.5·IQR. With IQR = 3.5, 1.5·IQR = 5.25, so fences are Q1 − 5.25 and Q3 + 5.25. Any observation outside those fences is often labeled an outlier.
- Example: if Q1 = 4.0 oz then Q3 = 7.5 oz, and fences are 4.0 − 5.25 = −1.25 oz (no realistic low outliers) and 7.5 + 5.25 = 12.75 oz.
Do you want help estimating Q1/Q3, detecting outliers in a data set, or converting this into a boxplot?
Useful consequences and how to use it
- Interpretation: the spread between the 25th percentile (Q1) and the 75th percentile (Q3) is 3.5 oz.
- You cannot recover Q1 or Q3 individually from the IQR alone; you need one of the quartiles (or the median plus additional info).
- Outlier fences (Tukey rule): lower fence = Q1 − 1.5·IQR, upper fence = Q3 + 1.5·IQR. With IQR = 3.5, 1.5·IQR = 5.25, so fences are Q1 − 5.25 and Q3 + 5.25. Any observation outside those fences is often labeled an outlier.
- Example: if Q1 = 4.0 oz then Q3 = 7.5 oz, and fences are 4.0 − 5.25 = −1.25 oz (no realistic low outliers) and 7.5 + 5.25 = 12.75 oz.
Do you want help estimating Q1/Q3, detecting outliers in a data set, or converting this into a boxplot?
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