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Is continuous distribution convert in discrete distribution?
If the question is asking if a continuous distribution can be converted to a discrete distribution, the answer is yes. Your age has a continuous distribution but in most cases, the information is recorded and analysed as if it were the whole number of years - a discrete distribution.
Does the median have 50 percent of the cases below only in a normal distribution?
No. By definition of the median, the median has 50 percent of the case below and 50 percent of the cases above. This has nothing to do with the cases being in a normal distribution.
Does a sample statistic always have a normal distribution?
No, many sample statistics do not have a normal distribution. In most cases order statistics, such as the minimum or the maximum, are not normally distributed, even when the underlying data themselves have a common normal distribution. The geometric mean (for positive-valued data) almost never has a normal distribution. Practically important statistics, including the chi-square statistic, the F-statistic, and the R-squared statistic of regression, do not have normal distributions. Typically, the normal distribution arises as a good approximation when the sample statistic acts like the independent sum of variables none of whose variances dominates the total variance: this is a loose statement of the Central Limit Theorem. A sample sum and mean, when the elements of the sample are independently obtained, will therefore often be approximately normally distributed provided the sample is large enough.
What is the difference of frequency distribution and relative frequency distribution?
A frequency distribution lists each value in the distribution and the number times it appears, while a relative frequency distribution reports the proportion of cases reporting each value
What situational problem in parametric test?
Parametric tests assume that data follow a specific distribution, typically a normal distribution, and that certain conditions, such as homogeneity of variances, are met. A situational problem arises when these assumptions are violated, such as when dealing with small sample sizes or skewed data, leading to inaccurate results. For example, using a t-test on data that are not normally distributed can result in misleading conclusions about group differences. In such cases, non-parametric tests may be more appropriate, as they do not rely on these strict assumptions.
Is continuous distribution convert in discrete distribution?
If the question is asking if a continuous distribution can be converted to a discrete distribution, the answer is yes. Your age has a continuous distribution but in most cases, the information is recorded and analysed as if it were the whole number of years - a discrete distribution.
Does the median have 50 percent of the cases below only in a normal distribution?
No. By definition of the median, the median has 50 percent of the case below and 50 percent of the cases above. This has nothing to do with the cases being in a normal distribution.
True or False If the population distribution is unknown in most cases the sampling distribution of the mean can be approximated by the normal dist. if the samples contain at least 30 observations.?
true
What is the word for uniform distribution?
The term for uniform distribution refers to a statistical distribution where every outcome is equally likely to occur. In a continuous uniform distribution, this is represented by a constant probability density function over a specified interval. In discrete cases, each individual outcome has the same probability, making it a flat probability mass function. In both cases, the distribution is characterized by a lack of bias toward any particular value.
When the population standard deviation is known the sample distribution is a?
When the population standard deviation is known, the sample distribution is a normal distribution if the sample size is sufficiently large, typically due to the Central Limit Theorem. If the sample size is small and the population from which the sample is drawn is normally distributed, the sample distribution will also be normal. In such cases, statistical inference can be performed using z-scores.
What is the difference between t test and z test?
Whereas a t-test is used for n30, where n=sample size. n < 30 or n > 30 is not entirely arbitrary; it is intended to indicate that n must be sufficiently large to use the normal distribution. In some cases, n must be greater than 50. Note, both the t-test and the z-test can only be used if the distribution from which the sample is being drawn is a normal distribution. A z-test can be used even if the distribution is not normal (but is not severely skewed) if n>30, in which case, we can safely assume that the distribution is normal.
Does a sample statistic always have a normal distribution?
No, many sample statistics do not have a normal distribution. In most cases order statistics, such as the minimum or the maximum, are not normally distributed, even when the underlying data themselves have a common normal distribution. The geometric mean (for positive-valued data) almost never has a normal distribution. Practically important statistics, including the chi-square statistic, the F-statistic, and the R-squared statistic of regression, do not have normal distributions. Typically, the normal distribution arises as a good approximation when the sample statistic acts like the independent sum of variables none of whose variances dominates the total variance: this is a loose statement of the Central Limit Theorem. A sample sum and mean, when the elements of the sample are independently obtained, will therefore often be approximately normally distributed provided the sample is large enough.
Why is age not normal distribution in statistics?
In a stable population, the number of people of any age must be smaller than the number of people in the age just below. This is because the difference between the two is the number of younger people who died at that age. Furthermore mortality rates are age dependent: after a relatively (or in some cases absolutely) high infant mortality, the rate drops until old age kicks in. As a reult the distribution is not normal. In a growing population the lower end of the distribution is large and so again not normal.
What is having one side of the distribution looking the same as the other side?
A normal distribution of data is one in which the majority of data points are relatively similar, meaning they occur within a small range of values with fewer outliers on the high and low ends of the data range. When data are normally distributed, plotting them on a graph results a bell-shaped and symmetrical image often called the bell curve. In such a distribution of data, mean, median, and mode are all the same value and coincide with the peak of the curve. However, in social science, a normal distribution is more of a theoretical ideal than a common reality. The concept and application of it as a lens through which to examine data is through a useful tool for identifying and visualizing norms and trends within a data set. Properties of the Normal Distribution One of the most noticeable characteristics of a normal distribution is its shape and perfect symmetry. If you fold a picture of a normal distribution exactly in the middle, you'll come up with two equal halves, each a mirror image of the other. This also means that half of the observations in the data falls on either side of the middle of the distribution. The midpoint of a normal distribution is the point that has the maximum frequency, meaning the number or response category with the most observations for that variable. The midpoint of the normal distribution is also the point at which three measures fall: the mean, median, and mode. In a perfectly normal distribution, these three measures are all the same number. In all normal or nearly normal distributions, there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean when measured in standard deviation units. For instance, in all normal curves, 99.73 percent of all cases fall within three standard deviations from the mean, 95.45 percent of all cases fall within two standard deviations from the mean, and 68.27 percent of cases fall within one standard deviation from the mean. Normal distributions are often represented in standard scores or Z scores, which are numbers that tell us the distance between an actual score and the mean in terms of standard deviations. The standard normal distribution has a mean of 0.0 and a standard deviation of 1.0. Examples and Use in Social Science Even though a normal distribution is theoretical, there are several variables researchers study that closely resemble a normal curve. For example, standardized test scores such as the SAT, ACT, and GRE typically resemble a normal distribution. Height, athletic ability, and numerous social and political attitudes of a given population also typically resemble a bell curve. The ideal of a normal distribution is also useful as a point of comparison when data are not normally distributed. For example, most people assume that the distribution of household income in the U.S. would be a normal distribution and resemble the bell curve when plotted on a graph. This would mean that most U.S. citizens earn in the mid-range of income, or in other words, that there is a healthy middle class. Meanwhile, the numbers of those in the lower economic classes would be small, as would the numbers in the upper classes. However, the real distribution of household income in the U.S. does not resemble a bell curve at all. The majority of households fall into the low to the lower-middle range, meaning there are more poor people struggling to survive than there are folks living comfortable middle-class lives. In this case, the ideal of a normal distribution is useful for illustrating income inequality.
What is the difference of frequency distribution and relative frequency distribution?
A frequency distribution lists each value in the distribution and the number times it appears, while a relative frequency distribution reports the proportion of cases reporting each value
What type of distribution is used to organize numeric data?
A common type of distribution used to organize numeric data is the normal distribution, which is characterized by its bell-shaped curve and symmetric properties around the mean. Additionally, other distributions such as the binomial distribution and Poisson distribution are used for specific types of data, particularly in cases involving discrete outcomes. These distributions help in understanding the underlying patterns and behaviors of the data, making it easier to analyze and interpret.
Is mean and median always very similar?
The mean and median are not always similar; their relationship depends on the distribution of the data. In a symmetrical distribution, such as a normal distribution, the mean and median are typically very close or identical. However, in skewed distributions, the mean can be significantly affected by outliers, causing it to differ from the median, which remains more representative of the central tendency. Thus, while they can be similar in certain cases, this is not universally true.
