Measures of

**spread**describe how similar or varied the set of observed values are for a particular variable (**data**item). Measures of**spread**include the range, quartiles and the interquartile range, variance and standard deviation.What is meant by the spread of data?

A measure of

**spread**, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population. It is usually used in conjunction with a measure of central tendency, such as the**mean**or median, to provide an overall description of a set of**data**.1

## What is the mathematical definition of a variance?

The

**variance**measures how far each number in the set is from the mean.**Variance**is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.2

## What is the difference between standard deviation and variance?

The

**standard deviation**is the square root of the**variance**. The**standard deviation**is expressed**in the**same units as the mean is, whereas the**variance**is expressed in squared units, but for looking at a distribution, you can use either just so long as you are clear about what you are using.3

## How do you calculate the spread of data?

**To find variance, follow these steps:**

- Find the mean of the set of data.
- Subtract each number from the mean.
- Square the result.
- Add the numbers together.
- Divide the result by the total number of numbers in the data set.

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## What does the variance measure?

In probability theory and statistics,

**variance**is the expectation of the squared deviation of a random variable from its mean. Informally, it**measures**how far a set of (random) numbers are spread out from their average value.5

## What is meant by the spread of data?

A measure of

**spread**, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population. It is usually used in conjunction with a measure of central tendency, such as the**mean**or median, to provide an overall description of a set of**data**.6

## What is the spread of the data in math?

A measure of

**spread**tells us how much a**data**sample is**spread**out or scattered. Measures of**spread**together with measures of location (or central tendency) are important for identifying key features of a sample to better understand the population from which the sample comes from.7

## What is the shape of the data?

The spread is the range of the

**data**. And, the**shape**describes the type of graph. The four ways to describe**shape**are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform. A graph with a single peak is called unimodal.8

## What is the center of the data?

The mean can be used to find the

**center**of**data**when the numbers in the**data set**are fairly close together. The median is the midpoint value of a**data set**, where the values are arranged in ascending or descending order.9

## What is the measure of location?

**Measures of location**.

**Measures of location**summarize a list of numbers by a "typical" value. The three most common

**measures of location**are the mean, the median, and the mode. The mean is the sum of the values, divided by the number of values.

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## What is the measure of center?

A

**measure**of central tendency (**measure of center**) is a value that attempts to describe a set of data by identifying the central position of the data set (as representative of a "typical" value in the set). We are familiar with**measures**of central tendency called the mean, median and mode.11

## Can variance be a negative number?

The

**variance**of a data set cannot be**negative**because it is the sum of the squared deviation divided by a positive value.**Variance can**be smaller than the standard deviation if the**variance**is less than 1.12

## What does the mean and standard deviation tell us?

**Standard deviation**is a number used to

**tell**how measurements for a group are spread out from the average (mean), or expected value. A low

**standard deviation**means that most of the numbers are very close to the average. A high

**standard deviation**means that the numbers are spread out.

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## What is standard deviation in math?

The

**Standard Deviation**is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma) The**formula**is easy: it is the square root of the Variance.14

## What is the deviation from the mean?

The

**average**of these numbers (6 ÷ 5) is 1.2 which is the**mean deviation**. Also called**mean**absolute**deviation**, it is used as a measure of dispersion where the number of values or quantities is small, otherwise standard**deviation**is used.15

## Why do we use range in statistics?

The

**range**is the size of the smallest interval which contains all the data and provides an indication of**statistical**dispersion. It is measured in the same units as the data. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.16

## What is the formula for variance and standard deviation?

The

**variance**(symbolized by S^{2}) and**standard deviation**(the square root of the**variance**, symbolized by S) are the most commonly used measures of spread. We know that**variance**is a measure of how spread out a data set is. It is calculated as the average squared**deviation**of each number from the mean of a data set.17

## What is the definition of center in math?

**Center**of a circle. The

**center**of a circle is the point which is equidistant from all points on the circle. In the figure below, C is the

**center**. The

**center**point is often used to label the whole circle. The figure below would be called "the circle C".

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## How do you calculate the variance?

**Method 1**

**Calculating Variance of a Sample**

- Write down your sample data set.
- Write down the sample variance formula.
- Calculate the mean of the sample.
- Subtract the mean from each data point.
- Square each result.
- Find the sum of the squared values.
- Divide by n - 1, where n is the number of data points.

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## What does the range of data tell you?

The

**range**can only**tell you**basic details about the spread of a set of data. By giving the difference between the lowest and highest scores of a set of data it gives a rough idea of how widely spread out the most extreme observations are, but gives no information as to where any of the other data points lie.