Statistics is as complex as it’s fascinating. This science also loves a direct approach, So let’s not waste time and have a little test of your skills, shall we? Take a quick glance at the list below and try to determine which of the following statistics are unbiased estimators of population parameters.
- Confidence interval
- Normal distribution
- Sample mean
- Sample variance
- Sample proportion
- Median
- Maximum likelihood
If you guessed 3, 4, and 5, you’re correct. The estimators that have expected value coinciding with the population parameter we need to assess are called unbiased and they’re probably the most specific ones out there. However, what are those variables that each of them determines? Let’s put on our thinking hats and find out.
First of all, what is a sample? That’s a selection of some part of the specific entity. In statistics, that usually refers to the group that’s supposed to represent the entire society. The samples gathered for different scientific purposes will vary depending on which question you need to answer. For example, no statistician will poll teenagers to find out how much money people in the US spend on their mortgage a year.
Let’s see which of the following statistics are unbiased estimators of population parameters
Sample mean is the average figure you get after analyzing all the answers that respondents gave. If your sample is representative, you’re going to receive realistic results that reflect what a specific life aspect is like for the entire population in the designated region or even an entire country.
Sample variance is, in a way, designed to support sample mean. This one is used to find the deviations in the points as compared to the average number. It’s also preferable to work with ungrouped data and make it grouped before finding the sample variance according to the corresponding formula. Nevertheless, your approach should depend on your goals since you can find variance for any kind of data.
Last but not least, sample proportion is the most unpredictable one on this list. It varies from one selected group to another, and there’s no knowing what it’s going to be for sure. Simply put, sample proportion is the percentage of those people who actually do what’s expected out of the general amount. It’s not difficult to estimate, but it will never remain the same, staying the characteristic of the specific group.
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So, those are the three estimators we were looking for. Once explained, they appear quite simple. When you were wondering (or knew at once) which of the following statistics are unbiased estimators of population parameters, you probably thought about the purpose that these values have. It’s a very practical goal—to determine the tendencies that reign in society. Some might find these tools a bit crude because they yield numbers that can become contestable, but we’d still get nowhere in statistics if we didn’t have these elements.