Final answer:
The answer to the question is (d) all of the above are properties of the mean, including changing any score affecting the mean, adding a constant altering the mean by that amount, and multiplying by a constant changing the mean by that factor.
Step-by-step explanation:
The question asks about properties of the mean in a dataset. The mean, also known as the average, is a summary measure that describes the central tendency of a set of numbers. The correct answer to the question is d) all of the above are properties of the mean.
- Changing the value of any score will change the mean. If you adjust any single number in a set of data, the mean will adjust accordingly since it is the sum of all values divided by the number of values.
- Adding a constant to each score increases the mean by that constant. This happens because each value in the dataset is increased by the constant, which then increases the total sum of the dataset by the constant multiplied by the number of values.
- Multiplying every score by a constant will multiply the mean by that constant. Multiplying each number means the sum of all values increases by a factor of that constant, as does the mean when you divide the increased sum by the original number of values.
These properties of the mean are fundamental and are reflected in its calculation, which involves both the sum of the dataset and the count of values within the dataset.