#### Solution By Steps
***Step 1: Arrange Data in Ascending Order***
Arrange the given data in ascending order: 3, 4.
***Step 2: Find the Median***
Since there are two data points, the median is the average of the two middle values.
Median = (3 + 4) / 2 = 3.5.
***Step 3: Largest Temperature Increase without Changing Median***
To keep the median unchanged, the largest temperature can increase up to the current median value.
Maximum increase = 3.5.
#### Final Answer
(a) Sample median: 3.5
(b) The largest temperature measurement could increase by 3.5 without changing the sample median.
#### Key Concept
Median
#### Key Concept Explanation
The median is the middle value of a dataset when arranged in ascending order. It is a robust measure of central tendency that is not affected by extreme values. In this case, the median is used to find the central value of the temperature data, and it helps determine how much the largest temperature can increase without altering the median.
Follow-up Knowledge or Question
What is the definition of the sample median in statistics?
How does an outlier affect the sample median compared to the mean in a dataset?
Can you explain the concept of the interquartile range (IQR) and its relationship with the median?
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