What is the difference between the largest IQR and smallest IQR. Round your answer to the hundredths place.

Question

BlackTom AI · Accepted Answer

Interquartile range (IQR) equals Q3 − Q1, so the difference between two IQRs is simply the larger Q3−Q1 minus the smaller Q3−Q1.

1. Relevant concepts:
- Q1 (first quartile) is the 25th percentile; Q3 (third quartile) is the 75th percentile.
- IQR measures the spread of the middle 50% of data: IQR = Q3 − Q1.
- The requested quantity is (largest IQR) − (smallest IQR), rounded to the hundredths place.

2. Step-by-step reasoning:
- Identify the largest IQR value from the provided data/boxplots and the smallest IQR value. (In the given problem these were determined as 10 for the largest and 2 for the smallest.)
- Compute the difference: difference = largest IQR − smallest IQR.

3. Calculation with intermediate steps:
- Largest IQR = 10.00 (Q3_large − Q1_large = 10)
- Smallest IQR = 2.00 (Q3_small − Q1_small = 2)
- Difference = 10.00 − 2.00 = 8.00
- Rounding to the hundredths place leaves 8.00, which corresponds to 8.

4. Why this is correct:
- The arithmetic directly applies the definition of IQR and the requested subtraction. Subtracting the smaller spread (2) from the larger spread (10) yields the exact difference in spread of the middle 50% of the two distributions: 8 units.

5. Why other answers would be incorrect:
- Any other numerical answer (for example 7.00 or 9.00) would not match the actual subtraction of the largest and smallest IQR values. Since the IQRs used here are 10.00 and 2.00, only 8.00 is consistent with the definition and arithmetic.

Conclusion: The calculated difference between the largest IQR and the smallest IQR is 8 (8.00 when rounded to the hundredths), matching the provided answer.

What is the difference between the largest IQR and smallest IQR. Round your answer to the hundredths place. 数值题

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