• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.375-385
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• 2014

This study compares the confidence interval estimation of population mean with that of population ratio, and considers whether these two estimations ensures consistency. As a result, this study suggests the following acquisition method of consistency : dealing with population mean and population ratio in the same mode, substituting the observed or experimental value of sample standard deviation for standard deviation in population in setting a confidence interval of both population mean and population ratio, and distinguishing population ratio $\hat{P}$ from its observed vale $\hat{p}$.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.445-459
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• 2005

Statistics education is considered within the mathematics curriculum and, thus, can be integrated into other areas of mathematics. However, statistical concepts and thinking skills have to be considered as very different from those of other areas. It is possible to make statistics more meaningful for the learner by making definitions or explanations of concepts in textbooks more clear and consistent. In 'Math I' and 'Probability & Statistics' of the 7th curriculum, the definitions of sample standard deviation are different, which might confuse students. In this study, firstly, some issues relevant to sample standard deviation concept are discussed through the analysis in terms of didactical situation and curriculum. Secondly, the characteristics of sample standard deviation concept as a scholarly knowledge are examined. Finally, the characteristics of didactic transposition of sample standard deviation concept in Japanese, American, and British textbooks are investigated and some suggestions are elicited.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.323-337
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• 2004

This article coined a general class of estimators for various measures in normal population when some' a priori' or guessed value of standard deviation a is available in addition to sample information. The class of estimators is primarily defined for a function of standard deviation. An unbiased estimator and the minimum mean squared error estimator are worked out and the suggested class of estimators is compared with these classical estimators. Numerical computations in terms of percent relative efficiency and absolute relative bias established the merits of the proposed class of estimators especially for small samples. Simulation study confirms the excellence of the proposed class of estimators. The beauty of this article lies in estimation of various measures like standard deviation, variance, Fisher information, precision of sample mean, process capability index $C_{p}$, fourth moment about mean, mean deviation about mean etc. as particular cases of the proposed class of estimators.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.1
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• pp.1-12
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• 2014

This article proposes a variable sampling interval (VSI) $\bar{X}$ control chart using weighted standard deviation (WSD) method for skewed populations. The WSD method decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts control limits and warning limits of a control chart in accordance with the direction and degree of skewness. A control chart constant is derived for estimating the standard deviation of skewed distributions with the mean of sample standard deviations. The proposed chart is compared with the conventional VSI $\bar{X}$ control chart under some skewed distributions. Simulation study shows that the proposed WSD VSI chart can control the in-control average time to signal (ATS) as an adequate level better than the conventional VSI chart, and the proposed chart can detect a decrease in the process mean of a quality characteristic following a positively skewed distribution more quickly than the standard VSI chart.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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• pp.151-157
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• 2019

This study is about the process capability index (PCI). In this study, we introduce several indices including the index $C_{PR}$ and present the characteristics of the $C_{PR}$ as well as its validity. The difference between the other indices and the $C_{PR}$ is the way we use to estimate the standard deviation. Calculating the index, most indices use sample standard deviation while the index $C_{PR}$ uses range R. The sample standard deviation is generally a better estimator than the range R. But in the case of the panel process, the $C_{PR}$ has more consistency than the other indices at the point of non-conforming ratio which is an important term in quality control. The reason why the $C_{PR}$ using the range has better consistency is explained by introducing the concept of 'flatness ratio'. At least one million cells are present in one panel, so we can't inspect all of them. In estimating the PCI, it is necessary to consider the inspection cost together with the consistency. Even though we want smaller sample size at the point of inspection cost, the small sample size makes the PCI unreliable. There is 'trade off' between the inspection cost and the accuracy of the PCI. Therefore, we should obtain as large a sample size as possible under the allowed inspection cost. In order for $C_{PR}$ to be used throughout the industry, it is necessary to analyze the characteristics of the $C_{PR}$. Because the $C_{PR}$ is a kind of index including subgroup concept, the analysis should be done at the point of sample size of the subgroup. We present numerical analysis results of $C_{PR}$ by the data from the random number generating method. In this study, we also show the difference between the $C_{PR}$ using the range and the $C_P$ which is a representative index using the sample standard deviation. Regression analysis was used for the numerical analysis of the sample data. In addition, residual analysis and equal variance analysis was also conducted.

• Journal of Sericultural and Entomological Science
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• v.15 no.1
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• pp.27-30
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• 1973

The present research has been carried out in an attempt to obtain fundamental data which contribute to enhansing the accuracy of cocoon reeling test and improving the method of it more effectively. The results obtained are as follows: 1. The standard deviation and coefficient of variation of percentage of reelability and of percentage of raw silk yield to the sample size tended to show a gradual decrease according to the increasing of the sample size. However, the significant differences in the standard deviation and coefficient of variation of percentage of reelability and of percentage of raw silk yield between the different sizes of the samples having more than 300 cocoons have not been observed according to their sizes. 2. The significant difference in the standard errors from percentage of reelability between the samples of 300 cocoons and 400 cocoons have not been observed. 3. The significant difference in the standad errors from percentage of raw silk yield between the samples of 300 cocoons, 500 cocoons and 600 cocoons have not been observed. 4. The significant difference in the standard deviation, the standard errors and coefficient of variation to the length of a bave between the different sizes of the samples have not been shown. 5. From the above result, it is estimated that the optimum sire of the sample for the cocoon reeling test is the 300 cocoons.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.197-210
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• 2005

In Korea, mathematics education has been taken according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare mathematics 1 textbooks for 11-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in accordance with textbooks and central limit theorem of sample mean under normal population.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.3
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• pp.205-212
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• 2004

This paper proposes the variables repetitive group sampling plan where the quality characteristic following normal distribution has upper or lower specification limit. The problem is formulated as a non-linear programming problem where the objective function to minimize is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level (AQL) and limiting quality level (LQL) under the operating characteristic curve. Sampling plan tables are constructed for the selection of parameters indexed by AQL and LQL in the cases of known standard deviation and unknown standard deviation. It is shown that the proposed sampling plan significantly reduces the average sample number as compared with the single or the double sampling plan.

• Analytical Science and Technology
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• v.13 no.2
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• pp.179-188
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• 2000

Trace elements in air samples artificially loaded on filters with urban dust and the bulk material of urban dust as an environmental sample were determined non-destructively using instrumental neutron activation analysis. Standard reference material (Urban Dust, SRM 1648) of the National Institute of Standard and Technology was used for the analytical quality control. The relative error for 37 elements was less than 15% and the standard deviation was less than 10%. 29 elements in the urban dust and 21 elements in the loaded filter sample were determined respectively. To evaluate the proficiency and reliability of the measurement, data intercomparison was performed and 39 analytical laboratories participated in the analysis using different analytical methods; neutron activation analysis, particle induced X-ray emission analysis, X-ray fluorescence analysis and atomic absorption spectrometry. Z-scores were calculated using the standard deviation of the laboratorie's mean as target standard deviation, and a good result was obtained that the values fall between -1 and +1 except some elements.

• Journal of Sericultural and Entomological Science
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• v.25 no.1
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• pp.44-50
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• 1983

The study was carried out to suggest on opinion of the standardization of size deviation in the existing raw silk testing method. 1. The present grade A of size deviation stipulates 4.61 to 5.80 of standard deviation for 50 to 69 denier of mean value, however, the 5.80 standard deviation with the mean values of 50 and 69 denier belong to different distribution. 2. It is reasonable that the variation coefficients of grade 2A should be lower than that of grade A. However, the present testing method shows larger variation in grade 2A than in grade A. This is illustrated 9.00 for 69 denier in grade 2A and 8.41 for 70 denier in grade A. 3. The size deviation value compares the quality of raw silk with different mean value. Therefore, the standard deviation is recommended to be replaced by the C.V. value in determining the grade of silk. 4. The C.V. have a tendency to increase with lower grades below 6A for the size deviation below 33 denier with some inconsistencies. The figures should be adjusted so that the C.V. inconsistencies size deviation below 33 denier will be corrected. 5. The standard deviation increases with size under the same grade for the size deviations above 33 denier, however, the C.V. does not vary greatly with size deviation. 6. To rectify the above-mentioned inconsistencies the C.V. conversion and curvilinear regresion correction is recommended to improve the present silk testing method 7. The table of size deviation standard are as follows: Suggested standard of size deviation, unit: C.V. Value