A disadvantage of using arithmetic mean to summarize a set of data is?
A. the arithmetic mean sometimes has two values.
B. it can used for interval and ratio data.
C. it is always different from the median.
D. it can be biased by one or two extremely small or large values.
D. It can be biased by one or two extremely small or large values.
The advantage is that it takes every number into account.
The disadvantage is that if you have a very large or very small number disproportionate to the rest then you calculations will be slightly off.
A. the arithmetic mean sometimes has two values
A. The arithmetic mean sometimes have two values
The correct answer is D. It can be biased by one or two extremely small or large values. Here's an explanation of how to arrive at this answer:
To understand the disadvantage of using the arithmetic mean to summarize a set of data, it's important to first understand what the arithmetic mean is. The arithmetic mean is commonly referred to as the average and is obtained by adding up all the values in a data set and dividing the sum by the total number of values.
Now, let's address the other options:
A. The arithmetic mean sometimes has two values: This statement is not entirely accurate. The arithmetic mean should have only one value, as it represents the central tendency of a data set.
B. It can be used for interval and ratio data: This statement is true. The arithmetic mean is a valid measure of central tendency for both interval and ratio data, which are two types of quantitative data.
C. It is always different from the median: This statement is false. While it is true that in some cases the arithmetic mean may be different from the median, it is not always the case. There are situations where the arithmetic mean and median might be equal, especially when the data set is symmetrically distributed.
D. It can be biased by one or two extremely small or large values: This is the correct answer. The arithmetic mean is sensitive to extreme values, also known as outliers. In the presence of outliers, the mean can be significantly influenced or skewed toward the direction of the outlier. Therefore, it may not accurately represent the typical value of a data set. In such cases, alternative measures, such as the median or trimmed mean, are often used to summarize the data, as they are less affected by extreme values.
In conclusion, the disadvantage of using the arithmetic mean to summarize a set of data is that it can be biased by one or two extremely small or large values.
If you post YOUR answer, we'll be glad to check it.
Think of the mean as a fulcrum (balance point) for a distribution of scores.
I hope this helps.