What is the significance of computing the absolute deviation in the experiment

To find the mean, add together all of the samples and divide by the number of samples. For example if your samples are 2, 2, 4, 5, 5, 5, 9, 10, 12, add them to get a total of Then divide by the number of samples, 9, to calculate a mean of 6. The second method of calculating the average is by using median. Arrange the samples in order from lowest to highest, and find the middle number.

From the example, the median is 5. The third method of calculating the average sample is by finding the mode. The mode is which ever sample occurs most. In the example, the sample 5 occurs three times, making it the mode. Calculate the absolute deviation from the mean by taking the mean average, 6, and finding the difference between the mean average and the sample. This number is always stated as a positive number. For example, the first sample, 2, has an absolute deviation of 4, which is its difference from the mean average of 6.

The mean absolute deviation has a few applications. The first application is that this statistic may be used to teach some of the ideas behind the standard deviation.

The mean absolute deviation about the mean is much easier to calculate than the standard deviation. It does not require us to square the deviations, and we do not need to find a square root at the end of our calculation.

Furthermore, the mean absolute deviation is more intuitively connected to the spread of the data set than what the standard deviation is. This is why the mean absolute deviation is sometimes taught first, before introducing the standard deviation. Some have gone so far as to argue that the standard deviation should be replaced by the mean absolute deviation. Although the standard deviation is important for scientific and mathematical applications, it is not as intuitive as the mean absolute deviation.

For day-to-day applications, the mean absolute deviation is a more tangible way to measure how spread out data are. Actively scan device characteristics for identification.

Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Share Flipboard Email. Table of Contents Expand. Example 1. Example 2. Example 3. Since we are only interested in the deviations of the scores and not whether they are above or below the mean score, we can ignore the minus sign and take only the absolute value, giving us the absolute deviation.

Adding up all of these absolute deviations and dividing them by the total number of scores then gives us the mean absolute deviation see below. Therefore, for our students the mean absolute deviation is Another method for calculating the deviation of a group of scores from the mean, such as the students we used earlier, is to use the variance. Unlike the absolute deviation, which uses the absolute value of the deviation in order to "rid itself" of the negative values, the variance achieves positive values by squaring each of the deviations instead.

Adding up these squared deviations gives us the sum of squares, which we can then divide by the total number of scores in our group of data in other words, because there are students to find the variance see below.

Therefore, for our students, the variance is As a measure of variability, the variance is useful. If the scores in our group of data are spread out, the variance will be a large number. Conversely, if the scores are spread closely around the mean, the variance will be a smaller number.

However, there are two potential problems with the variance.