# What is the definition of mean absolute deviation?

The

**mean absolute deviation**of a set of data**is**the average distance between each data value and the**mean**. The**mean**number of contacts stored and the distance each data value**is**from the**mean is**shown below. Each data value**is represented**by an ×.A.

### How do you find the deviation from the mean?

**To calculate the standard deviation of those numbers:**

- Work out the Mean (the simple average of the numbers)
- Then for each number: subtract the Mean and square the result.
- Then work out the mean of those squared differences.
- Take the square root of that and we are done!

#### Can the deviation from the mean be negative?

The standard**deviation can**never be**negative**– squaring all**deviations**results in a list of all positive numbers. ______5. Squaring every number in a list**will**square both the**mean**and the SD.#### 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.#### Is variance and standard deviation the same?

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.

B.

### How do you calculate the mean?

The

**mean**is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.#### What is the mean and median?

To find the**Median**, place the numbers you are given in value order and find the middle number. Example: find the**Median**of {13, 23, 11, 16, 15, 10, 26}. Put them in order: {10, 11, 13, 15, 16, 23, 26} The middle number is 15, so the**median**is 15. (If there are two middle numbers, you average them.)#### How do you work out a percentage?

To**calculate percentage**decrease: First:**work out**the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number then this is a**percentage**increase.#### Is the median the same as the 50th percentile?

In a population, at most half have values strictly less than the**median**and at most half have values strictly greater than it. The**median**is the 2nd quartile, 5th decile, and**50th percentile**. Since the**median**is the**same**as the second quartile, its calculation is illustrated in the article on quartiles.

Updated: 4th December 2019