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the normal distribution are a very important class of statistical distributions.all normal distributions are symmetric and have bell- shaped density curves with a single peak.both the normal and symmetrical distributions are u-shape and equal from both sides.
the normal distribution is considered the most prominent probability distribution in statistics.There are several reasons for this first, the normal distribution is very tractable analytically. that is a large number of results involving this distribution can be derived in explicit from.Second, the normal distribution arises as the outcome of the central limit theorem, which states that under mild conditions the large number of variables is distributed approximately normally.finally, the "bell" shape of the normal distribution marks it is a convenient choice for modeling a large variety of random variables encountered in practices.
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Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
What is the definition of 'bell curve'?
A bell curve is a graph that depicts a large rounded peak tapering away at each end of normal distribution. A bell curve is a mathematical concept with the curve concentrated in the center.
What is a single peaked distribution in statistics?
The classic example is a Bell curve. IQ testing (using the WAIS, or Wechsler Adult Intelligence Scale) yields a peak at the 100-105 IQ mark, with a downward curve on either side of the peak - representing the higher and lower IQ scores, respectively.
What is an example of a variable that is not normally distributed?
A variable that shows serious departure from the classic bell-shaped, or "Gaussian", curve is described as being not normally distributed. This departure could take the form of skew and/or kurtosis and/or multi modality.An example might be weekly wages. If you drew a histogram of a population's earnings you would most likely see a distribution skewed significantly toward the right. That is, toward the higher incomes.Another example is height. If you drew a histogram of a population's height you would see a bimodal distribution. One peak for males and another peak for females. The distribution of height for males and females might be normal when looked at individually, but not normal when you combine them.
What is the relationship between the relative size of the starndard deviation and the kurtosis of a distribution?
It is inversely proportional; a larger standard deviation produces a small kurtosis (smaller peak, more spread out data) and a smaller standard deviation produces a larger kurtosis (larger peak, data more centrally located).
Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
What odes kurtosis mean?
Kurtosis is a measure of the "peakedness" or thickness of the tails of a distribution compared to a normal distribution. A positive kurtosis indicates a distribution with heavier tails and a sharper peak, while a negative kurtosis indicates lighter tails and a flatter peak. Kurtosis helps to understand the shape of a distribution and the likelihood of extreme outcomes.
What is the expected value of the normal distribution?
The expected value of a normal distribution, also known as the mean, represents the central point around which the data is symmetrically distributed. For a normal distribution characterized by its mean (μ) and standard deviation (σ), the expected value is simply μ. This value indicates where the peak of the bell curve occurs and serves as a measure of central tendency for the distribution.
What happens in a normal distribution when the means are equal but the standard deviation changes?
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
What is the shape of a frequency distribution with an arithmetic mean of 12000 pounds a median of 12000 pounds and a mode of 12000 pounds?
The frequency distribution is likely to be symmetrical and bell-shaped, resembling a normal distribution. Given that the mean, median, and mode are all equal at 12,000 pounds, it suggests that the data is centered around this value with a balanced spread on either side. This indicates that the distribution has a single peak at the center, with a consistent frequency of values around the mean.
What are modes of distribution?
The data values with the highest frequency, gives the peak of the distribution graph.
What is a biphasic T wave and how does it differ from a normal T wave pattern on an electrocardiogram (ECG)?
A biphasic T wave on an ECG is when the T wave has two distinct peaks or phases instead of the usual single peak seen in a normal T wave pattern. This can indicate certain heart conditions or electrolyte imbalances. In contrast, a normal T wave has a single peak and is typically symmetrical in shape.
Is uniform distribution unimodal?
A uniform distribution is not considered unimodal because it has a constant probability density across its range, meaning there are no peaks or modes. In a unimodal distribution, there is one clear peak where the values cluster, while in a uniform distribution, all values within the specified range are equally likely. Therefore, it lacks a single mode.
What is the between skewness and kurtosis?
While skewness is the measure of symmetry, or if one would like to be more precise, the lack of symmetry, kurtosis is a measure of data that is either peaked or flat relative to a normal distribution of a data set. * Skewness: A distribution is symmetric if both the left and right sides are the same relative to the center point. * Kurtosis: A data set that tends to have a distant peak near the mean value, have heavy tails, or decline rapidly is a measure of high kurtosis. Data sets with low Kurtosis would obviously be opposite with a flat mean at the top, and a distribution that is uniform.
Is normal distribution symmetrical?
Yes. By definition. A normal distribution has a bell-shaped density curve described by its mean and standard deviation. The density curve is symmetrical(i.e., an exact reflection of form on opposite sides of a dividing line), and centered about (divided by) its mean, with its spread (width) determined by its standard deviation. Additionally, the mean, median, and mode of the distribution are equal and located at the peak (i.e., height of the curve).
Which factor does the width of the peak of a normal curve depend on?
The width of the peak of a normal curve depends primarily on the standard deviation of the distribution. A larger standard deviation results in a wider and flatter curve, indicating greater variability in the data, while a smaller standard deviation yields a narrower and taller peak, indicating less variability. Thus, the standard deviation is crucial for determining the spread of the data around the mean.
The is the greatest distance that particles in a medium move from their normal position when a wave passes.?
When measured, this distance (from normal to peak) is considered to be 1/2 of the amplitude. Amplitude is defined as the peak-to-peak distance.
