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If there are an odd number of values in the data set, include the median value in both halves when finding quartile values. For example, given the data set: {1, 4, 9, 16, 25, 36, 49, 64, 81} first find the median value, which is 25 (this is the second quartile). Since there are an odd number of values in the data set (9), we include the median in both halves. To find the quartile values, we much find the medians of: {1, 4, 9, 16, 25} and {25, 36, 49, 64, 81}. Since each of these subsets had an odd number of elements (5), we use the middle value.

50 TEACHER CERTIFICATION STUDY GUIDE The ultimate goal of sampling is to make generalizations about a population based on the characteristics of a random sample. Estimators are sample statistics used to make such generalizations. For example, the mean value of a sample is the estimator of the population mean. Unbiased estimators, on average, accurately predict the corresponding population characteristic. Biased estimators, on the other hand, do not exactly mirror the corresponding population characteristic.

Various factors affect the accuracy of sample statistics and the generalizations made from them about the larger population. Sample size is one important factor in the accuracy and reliability of sample statistics. As sample size increases, sampling error (standard deviation) decreases. Sampling error is the main determinant of the size of the confidence interval. Confidence intervals decrease in size as sample size increases. A confidence interval gives an estimated range of values, which is likely to include a particular population parameter.

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