• 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 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 $\hat{p}$.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1047-1061
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• 2015

Stratified random sampling is a powerful sampling strategy to reduce variance of the estimators by incorporating useful auxiliary information to stratify the population. Sample allocation is the one of the important decisions in selecting a stratified random sample. There are two common methods, the proportional allocation and Neyman allocation if we could assume data collection cost for different observation units equal. Theoretically, Neyman allocation considering the size and standard deviation of each stratum, is known to be more effective than proportional allocation which incorporates only stratum size information. However, if the information on the standard deviation is inaccurate, the performance of Neyman allocation is in doubt. It has been pointed out that Neyman allocation is not suitable for multi-purpose sample survey that requires the estimation of several characteristics. In addition to sampling error, non-response error is another factor to evaluate sampling strategy that affects the statistical precision of the estimator. We propose new sample allocation methods using the available information about stratum response rates at the designing stage to improve stratified random sampling. The proposed methods are efficient when response rates differ considerably among strata. In particular, the method using population sizes and response rates improves the Neyman allocation in multi-purpose sample survey.

• 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 the Korean Society of Fisheries and Ocean Technology
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• v.15 no.1
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• pp.1-3
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• 1979

The sand-eel, Ammodytes personatus GIRARD, "Kka-na-ri" is an important commercial fish inhabiting the coastal waters of Korea. The numbers of vertebrae (except urostyle) waR statistically analysezed based on the samples collected at three major fishing localitie" Jumunjin (East Sea), Geoje Island (southern coast) and Baegryeong Island (Yellow Sea) from May 1978 to June 1979. It was found that there was a very distinct difference in the numbers of vertebrae in the samples.rae in the samples.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.181-193
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• 2003

Without a sample standard deviation for an estimator of the population standard deviation u in a sample size computations, we often use some functions of a sample range (R) or interquartile range (IQR) by an estimator of $\sigma$. In order to avoid under-powered studies, these estimates must have a high probability of being greater than or equal to $\sigma$. In this paper, these probabilities of being greater than or equal to $\sigma$ are estimated for IQR for various parents distributions, and are compared with the probabilities for R/4 (Browne 2001). Alternative divisors (K) are explored and discussed for which the probabilities of R/K and IQR/K being greater than or equal to $\sigma$ is at least 95%.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.2
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• pp.124-136
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• 2006

The change pattern of the sediment grain size distribution information (median grain size(D50)) due to some gridding method and sampling density is analyzed with reference to the grid information estimated by the 90 sediment samples which was collected in the coastal water off the Baengnyeongdo Island, in June 2004. The standard deviation of absolute deviation (AD) estimated the selected gridding method shows 8.0 ${\mu}m$ at June, 2004 and 10 ${\mu}m$ November, 2004. The estimated statistical information of absolute deviation in comparison with the grid information of reference and changed sampling density shows that the AD mean error trends increase as the number of samples decrease. The AD mean error is below 10% in the case of the information estimation using 50-sample with reference to the 90-sample information. In this case, the sampling density is suggested as about 9 sediment samples per $km^2$, at coastal zone in Yoggipo port in the condition of the study area is 5.9 $km^2$.

• Journal of Korea Water Resources Association
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• v.56 no.12
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• pp.969-980
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• 2023

Since the 2000s, ensemble streamflow prediction (ESP) has been actively utilized in South Korea, primarily for hydrological forecasting purposes. Despite its notable success in hydrological forecasting, the original objective of enhancing water resources system management has been relatively overlooked. Consequently, this study aims to demonstrate the utility of ESP in water resources management by creating a simple hypothetical exercise for dam operators and applying it to actual multi-purpose dams in South Korea. The hypothetical exercise showed that even when the means of ESP are identical, different costs can result from varying standard deviations. Subsequently, using sampling stochastic dynamic programming (SSDP) and considering the capacity-inflow ratio (CIR), optimal release patterns were derived for Soyang Dam (CIR = 1.345) and Chungju Dam (CIR = 0.563) based on types W and P. For this analysis, Type W was defined with standard deviation equal to the mean inflow, and Type P with standard deviation ten times of the mean inflow. Simulated operations were conducted from 2020 to 2022 using the derived optimal releases. The results indicate that in the case of Dam Chungju, more aggressive optimal release patterns were derived under types with smaller standard deviations, and the simulated operations demonstrated satisfactory outcomes. Similarly, Soyang Dam exhibited similar results in terms of optimal release, but there was no significant difference in the simulation between types W and P due to its large CIR. Ultimately, this study highlights that even with the same mean values, the standard deviation of ESP impacts optimal release patterns and outcomes in simulation. Additionally, it underscores that systems with smaller CIRs are more sensitive to such uncertainties. Based on these findings, there is potential for improvements in South Korea's current operational practices, which rely solely on single representative values for water resources management.

• Journal of Food Hygiene and Safety
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• v.30 no.2
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• pp.127-131
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• 2015

This study aimed to calculate the required sample size to monitor food items during risk assessment studies. Based on a data set from a previous study (2,400 data points for heavy metal assessment from 17 food items), the required sample size was estimated by using a single equation with the standard deviation value, error range, and 95%-99% confidence intervals. The required sample size was calculated with each of the heavy metals for the assessment. The results showed that cadmium, lead, and mercury of required sample sizes for further monitoring were range of 7-90, 7-1, 062, and 11-238, respectively. We found that the required sample size varied depending on the standard deviation of the previous monitoring data. This study provides a basic method to determine the minimum sample size required in food monitoring to devise practical sampling strategies.

• The Korean Journal of Applied Statistics
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• v.31 no.4
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• pp.485-495
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• 2018

The CCC-r chart is more effective than traditional attribute control charts for monitoring high-quality processes. In-control process parameters are typically unknown and should be estimated when implementing a CCC-r chart. Phase II control chart performance can deteriorate due to the effect of the estimation error. In this paper, we used the standard deviation of average run length (ARL) as well as the average of ARL to quantify the between-practitioner variability in the CCC-r chart performance. The results indicate that the CCC-r chart requires larger Phase I data than previously recommended in the literature in order to have consistent chart in-control performance among practitioners.