The average deviation formula is used to characterize the dispersion among the given set of data. The average deviation is the average deviation of each observation from the mean value of the observation. The mean of the observations is calculated before the average deviation is calculated. The average deviation formula becomes a handy tool to quickly calculate the average deviation and reach the result very quickly. Let us study the average deviation formula using solved examples.
What Is Average Deviation Formula?
The average deviation formula is used to calculate the average deviation of the observation from the mean value of the observation. The average deviation formula for n number of observations is given below:
Average Deviation = 1/nΣ|\(x_i\) - x̅|
\(x_i\)= Data values in the given set.
x̅ is the mean.
n is the total number of data values
Let's take a quick look at a couple of examples to understand the average deviation formula, better.
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Example 1: Find the average deviation of the given data using the average deviation formula: 12, 14, 16, 18, 20, 22.
To find: average deviation
Given: n = 6
Finding mean of the given data:
x̅ = (12 +14 + 16 + 18 + 20 + 22)/6 = 17
Using the average deviation formula
Average deviation = (|12 - 17| + |14 - 17| + |16 - 17| + |18 - 17| + |20 - 17| + |22 - 17|)/6
= (5 + 3 + 1 + 1 + 3 + 5)/6 = 18/6 = 3
Average deviation = 3
Answer:Hence the average deviation of the given data is 3.
Example 2: Find the average deviation of the given data using the average deviation formula: 33, 44, 55, 66, 77, 88, 99.
To find: average deviation
Given: n = 7
Goinding mean of the given data:
x̅ = (33 + 44 + 55 + 66 + 77 + 88 + 99)/7 = 66
Using the average deviation formula,
Average deviation = (|33 - 66| + |44 - 66| + |55 - 66| + |66 - 66| + |77 - 66| + |88 - 66| + |99 - 66|)/7
Average deviation = 18.857
Answer: Hence the average deviation of the given data is 18.857.
Example 3: A football player played 5 games so far this season. The scoring numbers from each game are 14, 10, 9, 7, and 5. Determine the mean and calculate the average deviation.
Solution:The average of the score is = (14 + 10 + 9 + 7 + 5)/5 = 45/5 = 9
the average score = 9
To calculate the average deviation we need to calculate the deviation from the average for each game.
|14 - 9| = 5
|10 - 9| = 1
|9 - 9| = 0
|7 - 9| = 2
|5 - 9| = 4
Sum of variations = 5 + 1 + 0 + 2 + 4 = 12
Average deviation = 12/5 = 2.4
Answer: Hence the average deviation of the given data is 2.4
FAQs on Average Deviation Formula
How To Calculate the Mean of Data in Average Deviation Formula?
In the average deviation formula, the very first thing we calculate is the average of the given data set by dividing the sum of observations by a total number of observations.
How To Calculate the xi - x̅ in the Average Deviation Formula?
In the average deviation formula, the term (xi - x̅) is necessary to calculate as it gives the final value that is the average deviation of the given data. to calculate (xi - x̅) we first calculate the average of the given data then individually by subtracting the mean value from each observation the value of (xi - x̅) can be evaluated.
What Are the Steps To Calculate the Average Deviation Using Average Deviation Formula?
While calculating the average deviation using the average deviation formula we should follow the steps given below:
Calculate the average of the data observations given.
Calculate the value of (xi - x̅) deviation from the average.
Calculate the sum of all deviations (variations).
Calculate average deviation that is the ratio of the sum of variations to the total number of observations.