Concept:Removing extreme observations (smallest and largest) changes the sum and count, affecting the mean. The median stays the same because it is the middle value. Mode may change only if the removed extreme value is the most frequent value.
Explanation:First, consider the mean. Mean = sum of all values divided by the number of values. When you remove the highest and lowest values, both the sum and the count decrease. Therefore, the mean always changes.
Next, consider the median. For data arranged in descending order, the median is the middle value. Removing extreme values from both ends does not shift the middle position, so the median remains unaffected.
Finally, consider the mode. The mode is the value that appears most frequently. If the extreme observations are not the most frequent, removing them does not change the mode. However, if an extreme value itself is the mode (or tied for mode), removing one occurrence may reduce its frequency and possibly change the mode. Hence, the mode can be affected in some cases.
Among the given options, only mean and mode are affected, while median is not.
Answer:C. Mean and mode