Average Deviation Sum : 2

   The average deviation is defining that for finding or manipulating the average for the mean difference squared value in the given data. It is calculated by the enchanting of the sum for all the deviation standards divided by the total number of values.

             For measuring the average deviation of the statistics, find the mean for the given data using the formula,

                                                                   `barx = (sum_(k = 1)^n (x_n))/ (N)`

             Measure the mean difference value by using the calculated mean value by using the formula,

                                                                    `(x - barx)`

             Average Deviation is measured by taking the average for the founded mean difference of their squared value.

                                                  Average Deviation = `(sum_(K=1) ^n (x-barx)) / N `        

                                                      

 

Steps to calculate the Average Deviation Sum:

 

  • Give the average for all the given dimensions of the data set .
  • Give the difference of the initial value of the data and the average value we have found which is called as mean difference.
  • Take the all absolute value from this mean difference of the given data.
  • Repeat the steps 2 and 3 for all the other given values and find the mean difference to the data set.
  • For finding the average for the squared mean difference which is known as the average deviation of the given data set.         

 

Average deviation sum - Example Problems:

 

Average deviation sum - Problem 1:

Measure the average deviation for the given data set.  35, 32, 38, 36.

Solution:

     Mean: Formula for finding mean,

                                   `barx = (sum_(k = 1)^n (x_n))/ (n)`

                                   `barx = (32+35+36+38) / 4`

                                    ` barx = 141 / 4`

                                  ` barx =` 35.25

           Measure the deviation for the given data set from the mean,

                                   Deviation  =  `(x - barx)^2`

                                                   = `((32-35.25)^2+(35-35.25)^2+(36-35.25)^2+(38-35.25)^2) `

                                   Deviation = 18.75

             Measure the average deviation for the given data,

                                        Average Deviation = `(sum (x-barx)^2) / (n)`

                                                                          = `18.75 / 4`

                                       Average Deviation   =  4.6875

Average deviation sum - Problem 2:

Measure the average deviation for the given data set. 2, 4, 3, 3, 6, 4, 6.

Solution:

     Mean: Formula for finding mean value from the given data set is given by,

                                   `barx = (sum_(k = 1)^n (x_n))/ (n)`

     using the above formula find the average for the given values.

                                             `barx = (2+4+3+3+6+4+6)/7` 

                                            `barx = 28/ 7`

                                            ` barx` = 4

           Measure the deviation for the given data set from the mean,

                                   Deviation  =  `(x - barx)^2`

                                                      = ` ((2-4)^2+(4-4)^2+(3-4)^2+(3-4)^2+(6-4)^2+(4-4)^2+(6-4)^2) `                                                 

                                   Deviation = 14

             Measure the average deviation for the given data,

                                      Average Deviation = `(sum (x-barx)^2) / (n)`

                                                                     = `14 / 7`

                                     Average Deviation   = 2

                                

 

Average deviation sum - Practice Problems:

 

1 Measure the average deviation for the following 55.3, 56.6, 54.0, and 50.9.

Answer: Average Deviation = 4.47500

2. Measure the average deviation for the following data

Answer: Average Deviation = 2.

3. Find the average deviation for the following.4, 7, 5, 2, 8, 5, 6, 5,

Answer: Average Deviation   = 2.9375

4. Measure  the average deviation for the following data set. 32, 33, 35, 37.

Answer: Average Deviation   = 3.5625