Suppose a statistically independent sample of n Standard error of the sample mean Exact value In regression analysis, the term "standard error" refers either to the square root of the reduced chi-squared statistic or the standard error for a particular regression coefficient (as used in, say, confidence intervals). In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean. Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This forms a distribution of different means, and this distribution has its own mean and variance. The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. If the statistic is the sample mean, it is called the standard error of the mean ( SEM). The standard error ( SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value. For a ruler length of 30 meters, an error of about 2.6 millimeters will occur when the height difference between the two ends of the ruler is 0.4 meters, and the relative error is 1/11200.For the computer programming concept, see standard error stream. When measuring the horizontal distance, the steel tape measure should be kept as horizontal as possible, otherwise the distance increase error will occur. According to Hooke's law, a ruler length of 30 meters will produce a length error of ± 1.8 mm when the pull error is ± 5 kg. The elastic modulus of steel E = 2X106 KG / CM2. If you do not use a spring scale to measure the pulling force during measurement, an error will occur. The magnitude of the pulling force will affect the length of the steel ruler. Errors in temperature variation are taken into account in the ruler length equation. However, the same steel tape will still have a large length change in a large temperature difference environment, which affects Measurement results. The thermal expansion coefficient of a general steel tape is α = 1.25x10-5, which changes only 1 / 80,000 of the temperature difference per meter per degree. The main causes of errors in the use of steel tape measure are as follows: In order to avoid this change, it is required to use the tensile force marked on the ruler when using a steel tape measure. The ruler length will change when the ruler is subjected to different tensile forces. The length marked on the ruler is the nominal length, and the difference between it and the actual length is called the ruler length correction Δl. The more accurate steel tape measure must be tested at the factory and after a period of use, and the temperature, tensile force and rule length of the test must be indicated.
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