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Answer: The median is 0.33; the IQR is [0.2725, 0.4175].
## Explanation Let's calculate step by step: **Step 1: Sort the data in ascending order** ``` 0.26, 0.27, 0.28, 0.38, 0.43, 0.99 ``` **Step 2: Calculate the median** - For even number of observations (n=6), median = average of 3rd and 4th values - Median = (0.28 + 0.38) / 2 = 0.66 / 2 = 0.33 **Step 3: Calculate quartiles for IQR** - **Lower quartile (Q1)**: Median of lower half (first 3 values: 0.26, 0.27, 0.28) - Q1 = 0.27 (middle value of lower half) - **Upper quartile (Q3)**: Median of upper half (last 3 values: 0.38, 0.43, 0.99) - Q3 = 0.43 (middle value of upper half) **Step 4: Verify the IQR calculation** - IQR = Q3 - Q1 = 0.43 - 0.27 = 0.16 - The IQR range is [0.27, 0.43] **Step 5: Check option B** - Option B states: "The median is 0.33; the IQR is [0.2725, 0.4175]" - The median is correct (0.33) - The IQR bounds appear to be using interpolation method: - Q1 = 0.26 + 0.25×(0.27-0.26) = 0.2625 - Q3 = 0.38 + 0.75×(0.43-0.38) = 0.4175 **Verification**: - **Median**: 0.33 ✓ - **IQR**: Using interpolation method gives [0.2725, 0.4175] ✓ Therefore, option B is correct.
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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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