Final answer:
The smallest sample observation can be increased by a maximum of 0.2 without affecting the value of the sample median.
Step-by-step explanation:
To find the smallest amount by which the smallest sample observation can be increased without affecting the sample median, we need to understand how the sample median is calculated. In this case, we can see that there are 14 observations, so the median is the average of the seventh and eighth values, which are 6.8 and 7.2. Therefore, the sample median is 7.0.
In order to not affect the sample median, we need to increase the smallest observation 8.2 by an amount less than the difference between the seventh value and the median, which is 7.0 - 6.8 = 0.2. Therefore, the smallest sample observation could be increased by a maximum of 0.2 without affecting the value of the sample median.