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Is sample mean more efficient than sample median?
Two common ways to estimate the center of a set of data are the sample mean and the sample median. The sample mean is sometimes more efficient, but the sample median is always more robust. When the data come from distributions with a thin tail, like the normal, the sample mean is more efficient.
Is the sample median as good an estimator of the population mean as the sample mean?
Most simply, the sample median is a good estimator of the population mean when the population mean and population median are equal. If the population mean and population median are different, then the sample median estimates the population median and will likely not do a good job of estimating the population mean.
Why the sample mean is the best point estimate for the population mean?
“The variance of the sampling distribution of the median is greater than that of the sampling distribution of the mean. It follows that sample mean is likely to be closer to the population mean than the sample median. Therefore, the sample mean is a better point estimate of the population mean than the sample median.”
When is the sample median a good estimator of the population mean?
Most simply, the sample median is a good estimator of the population mean when the population mean and population median are equal. If the population mean and population median are different, then the sample median estimates the population median and will likely not do a good job of estimating the population mean.
What’s the difference between a sample and a population parameter?
None of your four options describes the difference between a single sample statistic and the population parameter. Population parameters are typically unknown (that is why we draw samples to calculate estimates and draw inferences) and so it doesn’t make sense to think about the difference between a single sample statistic and an unknown quantity.
When is it generally better to use median over mean?
For a lot of analysis, the mean is very useful. Indeed, if you’re trying to understand data that falls under a normal curve, the mean can tell you a lot of information, because it helps remove some statistical noise from the data and gives you an overall average score for the group.
When to use the mean or the mean?
Whenever a graph falls on a normal distribution, using the mean is a good choice. But if your data has extreme scores (such as the difference between a millionaire and someone making 30,000 a year), you will need to look at median, because you’ll find a much more representative number for your sample.