## The standard normal distribution

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

Converting a normal distribution into a z-distribution allows you to calculate the probability of certain values occurring and to compare different data sets.

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## Normal Distribution | Examples, Formulas, & Uses

In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center.

Normal distributions are also called Gaussian distributions or bell curves because of their shape.

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## What Is the Mean | How to Find It & Examples

The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”

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## How to find the median

The median is the value that’s exactly in the middle of a dataset when it is ordered. It’s a measure of central tendency that separates the lowest 50% from the highest 50% of values.

The steps for finding the median differ depending on whether you have an odd or an even number of data points. If there are two numbers in the middle of a dataset, their mean is the median.

The median is usually used with quantitative data (where the values are numerical), but you can sometimes also find the median for an ordinal dataset (where the values are ranked categories).

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## How to find the mode

The mode or modal value of a data set is the most frequently occurring value. It’s a measure of central tendency that tells you the most popular choice or most common characteristic of your sample.

When reporting descriptive statistics, measures of central tendency help you find the middle or the average of your data set. The three most common measures of central tendency are the mode, median, and mean.

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## How to find the interquartile range

In descriptive statistics, the interquartile range tells you the spread of the middle half of your distribution.

Quartiles segment any distribution that’s ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

Whereas the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set.

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## What is Variance? | Definition, Examples & Formulas

The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance tells you the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean.

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## How to Calculate Standard Deviation (Guide) | Formulas & Examples

The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.

A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.

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## How to find the range of a data set

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability.

Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set.

The range is calculated by subtracting the lowest value from the highest value. While a large range means high variability, a small range means low variability in a distribution.

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## Variability | Calculating Range, IQR, Variance, Standard Deviation

Variability describes how far apart data points lie from each other and from the center of a distribution. Along with measures of central tendency, measures of variability give you descriptive statistics that summarize your data.

Variability is also referred to as spread, scatter or dispersion. It is most commonly measured with the following:

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