Chapter 6 - The Normal Curve, Standardization, z-scores and the normal curve

standardization

the process of transforming data to a common scale or distribution in order to make meaningful comparisons. It involves adjusting variables by removing the effects of differences in scale, location, or dispersion. This allows for fair comparisons and analysis across different datasets or populations.

z score

also known as a standard score, measures the number of standard deviations a data point is from the mean of a distribution. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. This helps in comparing and analyzing data points from different distributions.

z distribution

also known as the standard normal distribution, is a probability distribution that is used in statistics. It is a continuous probability distribution with a mean of 0 and a standard deviation of 1. This is often used in hypothesis testing and calculating confidence intervals. It is also used to standardize data and calculate z-scores, which measure how many standard deviations a data point is from the mean. This is symmetric and bell-shaped, making it a useful tool in statistical analysis.

standard normal distribution

, is a specific type of probability distribution. It has a mean of 0 and a standard deviation of 1. The distribution is symmetric and bell-shaped, with the majority of the data falling within three standard deviations of the mean. It is commonly used in statistics and probability theory for various applications, such as hypothesis testing and calculating probabilities.

central limit theorem

regardless of the shape of the population distribution, the sampling distribution of the mean approaches a normal distribution as the sample size increases. This theorem is fundamental in statistics and is widely used in hypothesis testing and confidence interval estimation.

distribution of mean

the probability distribution of the sample means when repeatedly sampling from a population. It follows the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the population distribution. This is a fundamental concept in statistics and is used in various hypothesis testing and confidence interval calculations.

standard error

a measure of the variability or dispersion of a sample statistic, such as the mean. It quantifies the average amount of error between the sample statistic and the true population parameter. It is often used to estimate the precision or reliability of the sample statistic. This is calculated by dividing the standard deviation of the sample by the square root of the sample size. It is commonly represented by the symbol "SE" or "σ/√n" in statistical formulas.