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American women in terms of their physical heights.
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Which normal distribution is also the standard normal curve?
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Does the curve in a normal distribution stop at plus or minus 3 standard deviations?
No. The curve in a normal distribution goes on out to plus and minus infinity. You might never see any observations out there, but if you were to make an infinite number of observations, you theoretically would.
How would you characterize the distribution of scores in a normal distribution?
They are said to be Normally distributed.
Is it possible for sample not normal to be from normal population?
Yes. You could have a biased sample. Its distribution would not necessarily match the distribution of the parent population.
What shape would the probability distribution have for completely uncertain returns?
the variance is infinitely large and in the extreme case the probability distribution curve will simply be a horizontal line
Which normal distribution is also the standard normal curve?
The normal distribution would be a standard normal distribution if it had a mean of 0 and standard deviation of 1.
Does the curve in a normal distribution stop at plus or minus 3 standard deviations?
No. The curve in a normal distribution goes on out to plus and minus infinity. You might never see any observations out there, but if you were to make an infinite number of observations, you theoretically would.
What populations can you think of that would not likely have a normal distribution?
There are many populations that would not likely have a normal distribution. Endangered species or unsocial animals would be such populations.
How would you characterize the distribution of scores in a normal distribution?
They are said to be Normally distributed.
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.
Why it is important to determine the shape of data distribution before computing descriptive statistics?
You may be most familiar with the normal distribution (the Bell-shaped curve). The mean, mode and median of this distribution are all the same because it is symmetric. If, however, you take a sample from a distribution that is asymmetric in some way then the mean, mode and median will differ. You would need to decide which of these more effectively characterises the population. Then you would compute that descriptive statistic.
What does phenotypic distribution look like?
Look at the distribution of male height for instance. The mean of this normal distribution is around 5' 10''. So that means about 69% of men are within one standard deviation of this mean. If you saw a sample of men standing on bleachers it would look exactly as a Bell curve looks; normally distributed.
What does the phrase 'behind the curve' mean?
In a business sense, it usually means a new employee is not quite keeping up with the 'learning curve' required to perform a particular job. In other instances it would mean 'off the pace' or 'behind schedule'. The origin of the phrase refers to the statistical bell shaped curve also called the normal probability distribution; where to be 'behind the curve' is to be analogously in area of the graph to the left of the bell curve, to be 'ahead of the curve' analogously in the area of the graph to the right of the bell curve.
Is it possible for sample not normal to be from normal population?
Yes. You could have a biased sample. Its distribution would not necessarily match the distribution of the parent population.
What shape would the probability distribution have for completely uncertain returns?
the variance is infinitely large and in the extreme case the probability distribution curve will simply be a horizontal line
What are the types of normal distribution?
Generally, when we refer to the normal distribution, it is the standard, univariant normal distribution. We don't have a normal type 1, type 2, etc. However, there are closely related distributions, the truncated normal and the multivariant normal. A truncated multivariant normal would also be possible. See related links.
If you are given the equation of an normal sine curve how would you determine its period?
a normal sine curve exists with the formula Asin(Bx+C)+D. The formula to derive a phase shift would be such: 2pi/B (for whatever value B exists at). Thus, for a normal sine curve (sin(x) we would get 2pi/1, and arrive at 2pi for the period.
