. Elements of statistics. Statistics. DISTRIBUTION OF THE SAMPLE MEAN 157. 30 34 38 42 50 54 78 58 62 Xorx Figure Frequency distribution curve for a normal variate, X, and also for the sampling mean, x , for samples with n = 10. is very nearly equal to a/vn = 10/v 10 = , to two decimals, where the symbol n is used to denote the number of observations taken in the sample. The preceding discussion has suggested three features which are exhibited by a large number of sample means obtained from a normal population of numerical measurements. These features are: (a) Although it is impossib
. Elements of statistics. Statistics. DISTRIBUTION OF THE SAMPLE MEAN 157. 30 34 38 42 50 54 78 58 62 Xorx Figure Frequency distribution curve for a normal variate, X, and also for the sampling mean, x , for samples with n = 10. is very nearly equal to a/vn = 10/v 10 = , to two decimals, where the symbol n is used to denote the number of observations taken in the sample. The preceding discussion has suggested three features which are exhibited by a large number of sample means obtained from a normal population of numerical measurements. These features are: (a) Although it is impossible to predict the actual content of a particular future sample it may be possible to predict the type of fre- quency distribution which the sample means will follow, for example, a normal distribution. (6) The average sample mean will be of essentially the same magni- tude as the mean of the population sampled. (c) The sample means, Xi, will display less variability than the X's of the population. It is logical that the variabihty of the sample means—from sample to sample—should decrease as the size of the samples increases. It was suggested that a factor l/-\/n is involved here. The following theorem is given without proof because that proof is inappropriate to this book. The theorem is stated here for the purpose of replacing the indefiniteness of statements (a), (h), and (c) above with precise information which can be used in practice. Theorem. If a population of numerical measurements, X, con- forms to a normal frequency distribution with mean, m, and stand-. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Fryer, Holly Claire. Wiley
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