# 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:
1. Work out the Mean (the simple average of the numbers)
2. Then for each number: subtract the Mean and square the result.
3. Then work out the mean of those squared differences.
4. 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