Introduction for statistics categorical data tutorial:

In this article we will discuss about statistics correlation categorical data help. The correlation is an idea from statistics is calculate of how well trends in the expected values follow trends in past real values. The statistics correlation is a value between 0 and 1. If there is no relationship between the calculate values and the definite values the correlation coefficient is 0 or very low. Now we will discuss about formula of statistics categorical data tutorial. A tutorial is one procedure of convey information and may be used as a part of teaching.

 

Formula for statistics categorical data tutorial:

 

`"Correlation(r)"=[(NsumXY-(sumX)(sumY))/((sqrt([(NsumX^2)-(sumX)^2][NsumY^2-(sumY^2)]))]]`

Where
              N = Sum number of values
              X = 1st get
              Y = 2nd get
              sum XY = Addition of the 1st and 2nd achieve
              sum X = Addition of 1st achieve
              sum y = Addition of 2nd achieve
              sum x2 = Addition of square 1st achieve
              sum y2 = Addition of square 2nd get achieve

 

Example problems for statistics categorical data tutorial:

 

Statistics categorical data tutorial – Example 1:

Find the Correlation co-efficient of follow table

X

Y

62

3

63

3

64

3

65

4

66

4

 

Solution for statistics categorical data tutorial:

        Step 1: Count the number of values.
                     N = 5

        Step 2: Find XY, X2, Y2
                    See the below table     

 

X value

Y value

x* y

x*x

y*y

62

3

62*3 = 186

62*62 = 3844

3*3= 9

63

3

63*3 = 189

63*63 = 3969

3*3= 9

64

3

64*3 = 192

64*64 = 4096

3*3= 9

65

4

65*4 = 260

65*65 = 4225

4*4= 16

66

4

66*4 = 264

66*66 = 4356

4*4= 16

 

          Step 3: Find `sum` X, `sum` y, `sum` xy, `sum` x2, `sum` y2.

            sum x = 320 

            sum y = 17

            sum xy = 1091

            sum x2 = 20490

            sum y2 = 59

           Step 4: Now, Substitute in the above formula specified.

            `"Correlation(r)"=[(N sum XY-(sum X)(sum Y))/((sqrt([(N sum X^2)-(sum X)^2][N sum Y^2-(sum Y^2)])) ]]`

              =` [(5(1091) - (320)(17)) / ((sqrt([5(20490)-(320)^2][5(59)-(17)^2]))]] `

               = `(5455 - 5440)/sqrt([102450 - 102400] [295-289])`

               = `15/sqrt(50 xx6)`

               = `15/sqrt(300)`

               = `15/17.32`

               = 0.8660

            Answer is: 0.8660

Statistics categorical data tutorial – Example 2:

Calculate the statistics correlation of following table

X

86

87

88

89

90

Y

4.1

4.6

4.8

5

5.1

 

Solution 1 for solves statistics categorical data tutorial:

     Step 1:  Count the number of values.
                   N = 5

     Step 2:  Calculate XY, X2, Y2

                  See the below table

X

Y

x*y

x*x =` x^2`

y*y = `y^2`

86

4.1

 86*4.1 = 352.6

86*86= 7396

4.1* 4.1=16.81

87

4.6

 87*4.6 = 400.2

87*87= 7569

4.6* 4.6 =21.16

88

4.8

88*4.8 = 422.4

88*88= 7744

4.8* 4.8 =23.04

89

5

 89*5   =  445

89*89= 7921

   5*5 = 25

90

5.1

 90*5.1 = 459

 90*90= 8100

5.1* 5.1= 26.01

 

       Step 3: Find `sum` X, `sum` y, `sum` xy, `sum` x2, `sum` y2.

        `sum` x = 440

        `sum` y = 23.6

        `sum` xy = 2079.2

         `sum` x2 = 38730

        `sum` y2 = 112.02

      Step 4: Now, Substitute in the above formula specified.

      `"Correlation(r)"=[(NsumXY-(sumX)(sumY))/((sqrt([(NsumX^2)-(sumX)^2][NsumY^2-(sumY^2)])) ]]`

              = `[(5(2079.2) - (440)(23.6)) / ((sqrt([5(38730)-(440)^2][5(112.02)-(23.6)^2]))]]`

              = `(10396- 10384) / sqrt([193650 - 193600] [560.1 - 556.96])`              

              = `12 / sqrt(50 xx 3.14 )`

              = `12/ sqrt(157)`

              = `12/12.52`

              = 0.958

          Answer is 0.958