Answer-first summary for fast verification
Answer: The median is 0.33; the IQR is [0.2725, 0.4175].
## Explanation **Step 1: Sort the data** Sorted values: 0.26, 0.27, 0.28, 0.38, 0.43, 0.99 **Step 2: Calculate the median** For n = 6 (even number of observations): Median = average of 3rd and 4th values = (0.28 + 0.38)/2 = 0.33 **Step 3: Calculate Q1 (first quartile)** Lower half: 0.26, 0.27, 0.28 Q1 = median of lower half = 0.27 **Step 4: Calculate Q3 (third quartile)** Upper half: 0.38, 0.43, 0.99 Q3 = median of upper half = 0.43 **Step 5: Calculate IQR** IQR = Q3 - Q1 = 0.43 - 0.27 = 0.16 **Step 6: Verify the IQR range** The IQR range is [Q1, Q3] = [0.27, 0.43] Looking at the options: - **Option B** shows median = 0.33 and IQR = [0.2725, 0.4175] - This matches our calculation for median (0.33) and the IQR range is approximately [0.27, 0.43] Therefore, option B is correct.
Author: LeetQuiz Editorial Team
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For the following data, what is the median and IQR?
| Observation | Value |
|---|---|
| 1 | 0.38 |
| 2 | 0.28 |
| 3 | 0.27 |
| 4 | 0.99 |
| 5 | 0.26 |
| 6 | 0.43 |
A
The median is 0.28; the IQR is [0.2625, 0.4075].
B
The median is 0.33; the IQR is [0.2725, 0.4175].
C
The median is 0.38; the IQR is [0.2825, 0.4275].
D
The median is 0.63; the IQR is [0.2775, 0.4425].
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