Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators of population ranges? Why or why not?
The sample range is the difference between the largest and smallest values in a sample. It provides an estimate of the range of values in the population. However, the sample range may or may not target the value of the population range.
In general, sample ranges do not always make good estimators of population ranges. There are a few reasons for this:
1. Variability: The sample range is highly variable and can be influenced by extreme values or outliers in the sample. A single outlier can significantly impact the sample range, leading to an overestimate or underestimate of the population range.
2. Sample Size: The accuracy of the sample range as an estimator of the population range depends on the sample size. With a small sample size, the sample range may not adequately capture the variability of the population, leading to an inaccurate estimate.
3. Sampling Bias: If the sample is not representative of the population, the sample range may not accurately reflect the population range. For example, if the sample is obtained from a specific subgroup or has a biased selection process, it may not provide a reliable estimate of the population range.
Therefore, while the sample range can provide some information about the population range, it is not always a reliable or precise estimator. Other statistical measures, such as confidence intervals or hypothesis testing, may be more appropriate for estimating and making inferences about the population range.
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