平均偏差公式

平均偏差是分析给定数据可变性的有效方法。它是与中心点的所有偏差的平均值。平均偏差测量与平均值或中位数的距离。它也被称为平均绝对偏差（或）平均绝对偏差。

Mean– It is the average value of all the values in the data.

Median– It is the middle value in the data when the data is sorted from low to high.

计算平均偏差的步骤

步骤 1.计算给定数据的平均值或中值。

Mean can be calculated by adding all the numbers in the given data and this total sum is divided by the count of all digits.

Median value can be calculated by sorting the data from low to high or high to low and picking the middle value. If the total count of numbers in given data is odd then the middle value will be the median. If the total count is even then there will be two middle numbers for these 2 numbers calculate the average of those two and the resultant value is the median of that dataset.

步骤 2.计算与均值/中值的偏差。

The deviation value can be calculated by calculating the absolute difference between each value in the data and the result of Step-1 i.e., mean or median value.

步骤 3.求上一步结果的所有偏差之和。

步骤 4.使用数据集中所有值/偏差的偏差总和和计数找到所有偏差的平均值。最终得到的平均值是给定数据的平均偏差。

让我们看几个例子来更好地理解。

示例问题

问题 1：求数据 1、2、3、4、9、8、7、6 的平均偏差。

解决方案：

Step 1: Find the mean for the given data.

Mean=(Sum of all values)/(count of all values)

Mean = (1+2+3+4+9+8+7+6)/8

          = 40/8 => 5

Step 2: Find absolute deviations from data using mean.

Data	Mean	Deviation
1	5	abs(1-5) = 4
2	5	abs(2-5) = 3
3	5	abs(3-5) = 2
4	5	abs(4-5) = 1
9	5	abs(9-5) = 4
8	5	abs(8-5) = 3
7	5	abs(7-5) = 2
6	5	abs(6-5) = 1

Step 3: Sum of all deviations=4+3+2+1+4+3+2+1=20

Step 4: Find Average Deviation = sum of all deviations/count of values in data

                                                   = 20/8 => 5/4 => 1.25

So Average Deviation within the given data is 1.25

问题 2：求数据 1、2、3、4、9、8、7、6 的平均偏差。 （使用中位数找到中心点）

解决方案：

Step 1: Find median for the given data.

To find the median first we need to sort the given data either in ascending order or descending order.

Sorted data- 1,2,3,4,6,7,8,9

Here the size of the data set is even i.e., count=8.

So we got two middle values 4 & 6.

Find the average of these two numbers to find the median value.

Median = (4+6)/2 = 5

Step 2: Find absolute deviations from data using median.

Data	Median	Deviation
1	5	abs(1-5) = 4
2	5	abs(2-5) = 3
3	5	abs(3-5) = 2
5	5	abs(4-5) = 1
9	5	abs(9-5) = 4
8	5	abs(8-5) = 3
7	5	abs(7-5) = 2
6	5	abs(6-5) = 1

Step 3: Sum of all deviations = 4+3+2+1+4+3+2+1=20

Step 4: Find Average Deviation = sum of all deviations/count of values in data

                                                  = 20/8=> 5/4 => 1.25

So Average Deviation within the given data is 1.25

问题 3：求数据 10、25、30、14、39、18、17 的平均偏差。 （使用中位数找到中心点）

解决方案：

Step 1: Find median for the given data.

To find median first we need to sort the given data either in ascending order or descending order.

Sorted data- 10,14,17,18,25,30,39

Here the size of data set is odd i.e., count=7.

So we have only one middle value18 which is median.

Step 2: Find absolute deviations from data using median.

abs(10-18) = 8

abs(14-18) = 4

abs(17-18) = 1

abs(18-18) = 0

abs(25-18) = 7

abs(30-18) = 12

abs(39-18) = 21

Step 3: Sum of all deviations = 8+4+1+0+7+12+21=53

Step 4: Find Average Deviation=sum of all deviations/count of values in data

                                                 =53/7=> 7.57

So Average Deviation within the given data is 7.57

问题 4：求数据 10、20、30、40、39、28、17、10、20、26 的平均偏差。

解决方案：

Step-1 Find mean for the given data.

Mean=(Sum of all values)/(count of all values)

Mean=(10+20+30+40+39+28+17+10+20+26)/10

         =240/10=>24

Mean=24

Step-2 Find absolute deviations from data using mean.

abs(10-24) = 14

abs(20-24) = 4

abs(30-24) = 6

abs(40-24) = 16

abs(39-24) = 15

abs(28-24) = 4

abs(17-24) = 7

abs(10-24) = 14

abs(20-24) = 4

abs(26-24) = 2

Step 3: Sum of all deviations=14+4+6+16+15+4+7+14+4+2=86

Step 4: Find Average Deviation=sum of all deviations/count of values in data

                                                 =86/10=> 8.6

So Average Deviation within the given data is 8.6

问题 5：求数据 10、20、30、40、50 的平均偏差（使用均值/中值求中心点）

解决方案：

Step 1: Find the center point for the given data. 

As data is already in sorted order it is preferred to use the median to find the central point.

Here the size of the data set is odd i.e., count=5.

So we have only one middle value 30 which is the median.

Step 2: Find absolute deviations from data using the median.

abs(10-30)=20

abs(20-30)=10

abs(30-30)=0

abs(40-30)=10

abs(50-30)=20

Step 3: Sum of all deviations=20+10+0+10+20 =60

Step 4: Find Average Deviation=sum of all deviations/count of values in data

                                                 =60/5=>12

So Average Deviation within the given data is 12.