Certain statistics measures are unbiased. Which of the following show three unbiased estimators?
a. variance, standard deviation, median
b. mean, variance, proportion
c. mean, median, range
d. range, standard deviation, median
tbh im thinking b but im not sure either im still trying to figure it out
tbh im thinking b but im not sure either i neva seen a question like this
it should be b or d
I think it's either b or d, but I'm not sure.
To determine which of the following sets of statistics measures are unbiased estimators, we need to understand what an unbiased estimator is.
An unbiased estimator is a statistical measure that, on average, gives an estimate of a parameter that is equal to the true value of that parameter. It means that the estimator does not systematically overestimate or underestimate the true value.
Let's go through each option and determine whether the statistics measures listed in each are unbiased estimators:
a. Variance, standard deviation, median:
- Variance and standard deviation are both biased estimators. They tend to underestimate the true value of the population variance and standard deviation.
- The median is an unbiased estimator. It provides a nonparametric estimate of the population median, and it is not affected by extreme values and outliers.
b. Mean, variance, proportion:
- The mean is an unbiased estimator of the population mean. It provides an estimate that is generally close to the true value of the population mean.
- The variance is a biased estimator. It tends to underestimate the population variance.
- The proportion is an unbiased estimator when estimating the proportion or percentage of a binary attribute in a population.
c. Mean, median, range:
- The mean is an unbiased estimator of the population mean.
- The median is an unbiased estimator of the population median.
- The range is a biased estimator. It tends to underestimate the true range of values in the population.
d. Range, standard deviation, median:
- The range is a biased estimator of the true range.
- The standard deviation is a biased estimator of the true standard deviation.
- The median is an unbiased estimator of the true median.
Based on the explanations above, the correct answer is option c. The mean, median, and range are three unbiased estimators.