Question

Distinguish between simple and weighted average and state the circumstances under which the latter should be employed.

a) Simple average considers all values equally, while weighted average assigns different weights to values based on importance. Use weighted average for skewed datasets.
b) Simple average assigns different weights to values based on importance, while weighted average considers all values equally. Use simple average for normal distributions.
c) Both simple and weighted averages are identical and can be used interchangeably.
d) Simple average is suitable for small datasets, while weighted average is suitable for large datasets.

Answer 1

Simple average treats all values equally, while weighted average accounts for the importance of each value. Weighted average should be used when the importance of data points varies or when there are outliers that could skew a simple average.

Step-by-step explanation:

The simple average (or arithmetic mean) and the weighted average are both measures of central tendency, but they are calculated differently and used in different circumstances. A simple average considers all values equally and is calculated by adding up all the values and dividing by the number of values. On the other hand, a weighted average assigns different weights to values to reflect their importance or frequency. This means that some values will have more influence on the average than others.

You should employ a weighted average under certain circumstances, for example when dealing with a dataset where not all data points should contribute equally to the final average. This can occur if you're calculating a student's overall grade based on assignments with different levels of importance or when averaging financial data where certain investments carry more risk and therefore have a different weight in the portfolio.

It is important to use a weighted average when the data is skewed or contains outliers since a simple average may not provide an accurate representation of the data set's central tendency. Outliers can disproportionately affect the simple average, which is why the weighted average or median is often preferred in such cases.