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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.​

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kwalabapuzo

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Carmelo Hoeger

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8y ago

It is a distribution which is symmetric about its mean and median.

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Q: What is having one side of the distribution looking the same as the other side?
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Value of distribution coefficient of hemoglobin?

lol...u seem to be studying in swinburne?? may be coincidence...! I was looking for the same stuff :P


Why Normal distribution is better then other distributions in statistics?

The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.


What is symmetric distribution?

It is a probability distribution in which the probability of the random variable being in any interval on one side of the mean (expected value) is the same as for the equivalent interval on the other side of the mean.


What kind of distribution is a standard z distribution?

It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.


How to identify the the shape of probability distribution?

You cannot. There are hundreds of different distributions. The shapes of the distributions depend on their parameters so that the same distribution can be symmetric when the parameters have some specific value, but is highly skewed - in either direction - for other values.

Related questions

Is the F distribution same as t distribution?

No they are not the same.


Value of distribution coefficient of hemoglobin?

lol...u seem to be studying in swinburne?? may be coincidence...! I was looking for the same stuff :P


What is the same as the 50th percentile of a distribution?

The Median is the same as the 50th percentile of a distribution.


Is Gaussian distribution same as normal distribution?

yes


Why Normal distribution is better then other distributions in statistics?

The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.


What is the distribution when the mean median and mode are the same?

The normal distribution.


Can mean and median have same values?

Yes, they can.Yes, they can. In a symmetric distribution they will be the same.


Are the mean median and the mode the same in a unimodal symmetrical distribution?

No they are not the same in a unimodal symmetrical distribution and they will never be


What is symmetric distribution?

It is a probability distribution in which the probability of the random variable being in any interval on one side of the mean (expected value) is the same as for the equivalent interval on the other side of the mean.


Is the uniform probability distribution is symmetric about the mode?

Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable. * * * * * The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist. The distribution cannot, therefore, be symmetric about something that does not exist.


What are the properties of poisson distribution?

It is a discrete distribution in which the men and variance have the same value.


Does tile have to be the same way in two different rooms?

Tile does not have to be laid the same way in two different rooms. Having said that, if the two rooms join each other the tile really should be laid in the same fashion in both to avoid looking esthetically incorrect.