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Mean absolute deviation (MAD) is a statistical measure that quantifies the dispersion of a dataset. It provides insights into how much the data points deviate from the mean. Unlike other measures of dispersion, such as variance or standard deviation, MAD is less sensitive to extreme values, making it a robust measure in analyzing datasets with outliers. In this article, we will explore how to calculate the mean absolute deviation for ungrouped data, step-by-step. This will equip you with the necessary tools to better understand and analyze datasets, ultimately leading to more accurate interpretations and decisions based on the data.
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When working with data, there are different ways to look at the range and spread of values in a set, with the most common being the mean. Most of us have learned that to calculate the mean, you need to find the sum of the set and then divide it by the number of values in the group. The more advanced form of math is calculating the mean absolute deviation. This calculation shows how close the values in the set are to the average. To calculate the mean absolute deviation from the mean of the data set, calculate the absolute deviation of each data point from the mean, and then average those deviations.
Steps
Calculate the average
- For example, we have a data set consisting of the values 6, 7, 10, 12, 13, 4, 8 and 12. This set is small enough to count, you can easily see that there are 8 numbers in the set. .
- In statistics, the variable WOMEN{displaystyle N} or n{displaystyle n} commonly used to represent the number of values in a data set.
- Σx=6+7+ten+twelfth+13+4+8+twelfth=72{displaystyle Sigma x=6+7+10+12+13+4+8+12=72}
- μ=ΣxWOMEN=728=9{displaystyle mu ={frac {Sigma x}{N}}={frac {72}{8}}=9}
Calculate mean absolute deviation
- Fill in the data points of the problem in the first column.
- In the example of the article, the offsets would be:
- 6−9=−3{displaystyle 6-9=-3}
- 7−9=−2{displaystyle 7-9=-2}
- ten−9=first{displaystyle 10-9=1}
- twelfth−9=3{displaystyle 12-9=3}
- 13−9=4{displaystyle 13-9=4}
- 4−9=−5{displaystyle 4-9=-5}
- 8−9=−first{displaystyle 8-9=-1}
- twelfth−9=3{displaystyle 12-9=3}
- To check if these results are correct, you can sum the values in the deviation column. If this sum is zero, you are correct. If the sum is non-zero, it’s likely that the mean is incorrect, or that you miscalculated one or more deviations. Let’s retrace each calculation.
- In mathematics, absolute value is used to measure distance or size, not in terms of direction.
- To find the absolute value, simply remove the negative sign from each number in the second column and fill in the third column as follows:
- x.....(x−μ).....|(x−μ)|{displaystyle x…..(x-mu )…..|(x-mu )|}
- 6……….−3……….3{displaystyle 6………-3……….3}
- 7……….−2……….2{displaystyle 7……….-2……….2}
- 10…………1…………1{displaystyle 10………1……….1}
- 12………3……….3{displaystyle 12………3……….3}
- 13………4……….4{displaystyle 13………4……….4}
- 4……….−5………5{displaystyle 4……….-5……….5}
- 8……….−1………1{displaystyle 8………-1……….1}
- 12………3……….3{displaystyle 12………3……….3}
- Continuing this example, the average absolute deviation would be:
- 3+2+first+3+4+5+first+38=228=2,75{displaystyle {frac {3+2+1+3+4+5+1+3}{8}}={frac {22}{8}}=2.75}
- As in the data set above, the mean is 9 and the mean distance from the mean is 2.75. Note that some values will be closer to the average than 2.75, others will be further away. However, that is the average distance.
Advice
- Regular practice will help you calculate faster.
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 9,891 times.
When working with data, there are different ways to look at the range and spread of values in a set, with the most common being the mean. Most of us have learned that to calculate the mean, you need to find the sum of the set and then divide it by the number of values in the group. The more advanced form of math is calculating the mean absolute deviation. This calculation shows how close the values in the set are to the average. To calculate the mean absolute deviation from the mean of the data set, calculate the absolute deviation of each data point from the mean, and then average those deviations.
In conclusion, calculating the Mean Absolute Deviation (MAD) is a straightforward process when dealing with ungrouped data. By following a few simple steps, one can determine the average absolute difference between each data point and the mean. This measure of dispersion provides valuable insights into the spread or variability of the data set. Through the use of absolute values, the MAD ensures that both positive and negative deviations are considered equally, making it a reliable measure for analyzing ungrouped data. It is an important tool in statistics and can be used to compare the variability of different data sets or to assess the consistency of a given data set. With its ease of calculation and interpretability, the MAD is a useful tool for researchers, analysts, and decision-makers in various fields.
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