## 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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## Understanding and calculating variance

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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## Understanding and calculating standard deviation

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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## Measures of variability

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:

## An introduction to inferential statistics

While descriptive statistics summarize the characteristics of a data set, inferential statistics help you come to conclusions and make predictions based on your data.

When you have collected data from a sample, you can use inferential statistics to understand the larger population from which the sample is taken.

Inferential statistics have two main uses:

• making estimates about populations (for example, the mean SAT score of all 11th graders in the US).
• testing hypotheses to draw conclusions about populations (for example, the relationship between SAT scores and family income).

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## What is a ratio scale of measurement?

A ratio scale is a quantitative scale where there is a true zero and equal intervals between neighboring points. Unlike on an interval scale, a zero on a ratio scale means there is a total absence of the variable you are measuring.

Length, area, and population are examples of ratio scales.

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## Interval data: definition, examples, and analysis

Interval data is measured along a numerical scale that has equal distances between adjacent values. These distances are called “intervals.”

There is no true zero on an interval scale, which is what distinguishes it from a ratio scale. On an interval scale, zero is an arbitrary point, not a complete absence of the variable.

Common examples of interval scales include standardized tests, such as the SAT, and psychological inventories.

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## Ordinal data: examples, collection, and analysis

Ordinal data is classified into categories within a variable that have a natural rank order. However, the distances between the categories are uneven or unknown.

For example, the variable “frequency of physical exercise” can be categorized into the following:

There is a clear order to these categories, but we cannot say that the difference between “never” and “rarely” is exactly the same as that between “sometimes” and “often”. Therefore, this scale is ordinal.

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## How to collect and analyze nominal data

Nominal data is labelled into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.

For example, preferred mode of transportation is a nominal variable, because the data is sorted into categories: car, bus, train, tram, bicycle, etc.

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