Mean Deviation Formula

Mean Deviation Formula

We define the data set’s mean deviation as the value that indicates how distant each data point is from the data set’s centre point. The Mean, Median, or Mode can all serve as the data set’s centre point. Thus, the mean deviation of a data set is defined as the average of the deviations of all the data in the set from the data set’s centre. We can calculate mean deviation for both grouped and ungrouped data. Mean deviation is the arbitrary shift in values from the data set’s centre point.

What is Mean Deviation?

The mean deviation of a standard distribution is the average of its deviations from the central tendency. The Central Tendency can be calculated using the data’s Arithmetic Mean, Median, or Mode. It is used to demonstrate how distant the observations are from the data’s centre point (which might be mean, median, or mode).

We simply define the mean deviation of the given data distribution as the average of the observations’ absolute departures from a suitable central value. The acceptable central value might be the mean, median, or mode of any of the data’s fundamental trends.

Mean Deviation Definition

The term “Mean Deviation Formula” refers to the average absolute deviation. The average absolute deviation is defined as the average of the absolute departures from the data’s central point. The Mean Deviation Formula, median, or mode can be used to calculate the centre point.

A data set’s average deviation is the sum of all deviations from a given central point. It is a statistical tool for calculating the distance from a Mean Deviation Formula or median, where the Mean Deviation Formula is the average value of all numbers in the data set, and the median is the exact middle number when the data set is ordered from the lowest to the highest number. It is also possible to refer to the average deviation of a data set as the mean absolute deviation (MAD) or average absolute deviation.

Although average deviation can be calculated manually when working with relatively small amounts of data, bigger datasets often necessitate using specific software that executes the calculations once you enter the initial data.

The standard deviation of a data set is also a measure of variability because it represents the extent of the deviation between all values in the data set. The key distinction between the two is that when computing the average deviation, the values obtained by subtracting the mean from the value of each data point are only written as absolutes. When calculating standard deviation, the resulting numbers are squared rather than written in absolutes. The mean of all the squared values must then be calculated. The standard mean is the square root of that mean.

The standard deviation is a measure of variability that is increasingly frequently employed. It is also a common tool for calculating the volatility of financial instruments and prospective investment returns. Higher volatility often indicates an increased risk of an investment producing a loss, implying that an investor who takes on the risk of high-volatility security should expect a high return. Although less frequently than the standard deviation, the average deviation is also used as a financial tool.

Mean Deviation Formula

The average of the absolute deviations of the observations’ or values’ values from a useful average is known as the mean deviation. The Mean Deviation Formula, median, or mode are all acceptable averages to use. The term means absolute deviation is another name for it.

Mean Deviation Formula for Ungrouped Data

Data that has not been sorted or categorised into groups and is still in its raw form is known as ungrouped data. Individual data series are typically included in ungrouped data.

Mean Deviation = ∑_iⁿ (x_i – x̄) / n

where,
x_i represents the ith observation
x̄ represents any central point (mean, median, or  mode)
n represents the number of observations given in the data set

Mean Deviation Formula for Grouped Data

Data that has been structured and categorised into groups is referred to as grouped data. Discrete and continuous frequency distributions are used to group data.

Class intervals are the main component of this kind of grouped data. The continuous frequency distribution indicates how often an observation is repeated within each interval.

Mean Deviation = ∑_iⁿ (x_i – x̄) / ∑_iⁿ f_i

Where x̄ = ∑_iⁿ x_if_i / ∑_iⁿf_i

Mean Deviation about Mean

The deviation is a metric used in statistics and mathematics to determine the discrepancy between an observed value and an expected value of a variable. The deviation can be defined as the distance from the centre point. In a similar manner, the mean deviation is employed to determine how far the values deviate from the data set’s median.

We group the data and describe the frequency distribution of each group in order to provide it in a more condensed format. Class intervals are the names of these teams.

Data can be grouped in two different ways: Distributed Frequency Analysis and Distribution of Frequency Continuously

Mean Deviation about Median

One of the measurements of dispersion in statistics is Mean Deviation Formula. Any one of the central tendency measures can be used to determine this. The median and mean deviation from the mean, however, are the statistical factors that are most frequently applied.

Mean Deviation = ∑_iⁿ (x_i – M) / n

Where M represents the middle point or median of the data set and is calculated as,

• For n = odd terms,
  • M = [(n + 1)/2]^th observation
• For n = even terms,
  • M = [(n/2)^th + (n/2 + 1)^th] / 2

Mean Deviation about Mode

The value that occurs the most frequently in a given data collection is defined as the mode. The value in a data collection that appears the most frequently is the mode. The mode can be determined similarly to ungrouped data. The modal class has the following characteristics: l is its lower value, h is its size, f is its frequency, f1f1 is that of the modal class’s predecessor, and f2f2 is its successor.

Mean Deviation = ∑_iⁿ (x_i – M) / n

Where M represents the mode of the data set.

How to Calculate Mean Deviation?

The general procedures remain the same regardless of whether the mean deviation from the mean, median, or mode must be found. The only change will be in the formulas used to determine the mean, median, or mode based on our data type. Assume you need to calculate the mean deviation from the mean for the data sets 10, 15, 17, 15, 18, and 21. Determine the mean, mode, or median of the provided data values. Subtract the value of the central point (here, mean’s) from each data point.

Now take the absolute of the values obtained in step 2. Take the sum of all the values obtained in step 3. Divide this value by the total number of observations. It results in the mean deviation as there are 6 observations hence, 16 / 6 = 2.67, which is the mean deviation about the mean.

Mean Deviation and Standard Deviation

The Mean Deviation Formula is calculated using the central points (mean, median, or mode). To calculate the standard deviation, we only use the mean. The Mean Deviation Formula is determined by taking the absolute value of the deviations. We use the square of the deviations to calculate the standard deviation. It is not utilised as frequently. It is the most widely used and most typical measure of variability. Mean absolute deviation is utilised if there are more outliers in the data. Standard deviation is utilised if the number of outliers in the data is lower.

Merits and Demerits of Mean Deviation

A statistical measure called mean deviation have benefits and drawbacks. It is used to check the distribution of data about the central value.

Merits of Mean Deviation

Mean Deviation Formula is a valuable measure because it can compensate for the inadequacies of other statistical measures. It is straightforward to compute and understand. It is not adversely affected by outliers. It’s very common in business and trade. When compared to other statistical metrics, it exhibits the fewest sample variations. It is a useful comparison metric because it is based on deviations from the mean.

Demerits of Mean Deviation

Mean Deviation Formula cannot be algebraically treated further. As a result, usability may suffer. It is not strictly defined because it can be calculated in terms of Mean Deviation Formula, median, and mode. This metric is rarely used to assess data in sociological studies. We use the absolute value, disregarding both positive and negative indicators. This can result in inaccuracies in the outcome.