Check whether the program is working correctly or not for data set (i).

Question

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Answer 1

Question

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

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Answer 2

Question

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

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Answer 3

Question

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

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Answer 4

Question

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

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Answer 5

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

Answer 6

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

Answer 7

Chapter 9.6, Problem 6RE

(i)

To determine

Check whether the program is working correctly or not for data set (i).

Answer 8

(i)

Expert Solution

Answer to Problem 6RE

Yes, the program is working as correctly.

Answer 9

(i)

Expert Solution

Answer 10

(i)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+1+4+3+7+5+67=287=4

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(2−4)2+(1−4)2+(4−4)2+(3−4)2+(7−4)2+(5−4)2+(6−4)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	2	1−42=−1.5	2−42=−1.0	1.5
2	1	2−42=−1.0	1−42=−1.5	1.5
3	4	3−42=−0.5	4−42=0	0
4	3	4−42=0.0	3−42=−0.5	0
5	7	5−42=0.5	7−42=1.5	0.75
6	5	6−42=1.0	5−42=0.5	0.5
7	6	7−42=1.5	6−42=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.5)7=5.757=0.8214

Thus, the value of r is 0.8214

The given correlation value (0.8214) and the estimated correlation value (0.8214) both are same. Therefore, yes the program is working as correctly.

Answer 13

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.

Answer 14

(ii)

To determine

Explain whether the program is working as correctly or not for data set (ii).

Answer 15

(ii)

Expert Solution

Answer to Problem 6RE

No, the program is not working correctly.

Answer 16

(ii)

Expert Solution

Answer 17

(ii)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=1+2+3+4+5+6+77=287=4

The standard deviation of x is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(1−4)2+(2−4)2+(3−4)2+(4−4)2+(5−4)2+(6−4)2+(7−4)27=9+4+1+0+1+4+97=4=2

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=5+4+7+6+10+8+97=497=7

The standard deviation of y is obtained as follows:

SD=Sum of ((Entry−Average)2)Total number of data values=(5−7)2+(4−7)2+(7−7)2+(6−7)2+(10−7)2+(8−7)2+(9−7)27=4+9+0+1+9+1+47=4=2

The value of r is obtained below:

x	y	x in standard units	y in standard units	(x in standard units) × (y in standard units)
1	5	1−42=−1.5	5−72=−1.0	1.5
2	4	2−42=−1.0	4−72=−1.5	1.5
3	7	3−42=−0.5	7−72=0	0
4	6	4−42=0.0	6−72=−0.5	0
5	10	5−42=0.5	10−72=1.5	0.75
6	8	6−42=1.0	8−72=0.5	0.50
7	9	7−42=1.5	9−72=1.0	1.5

r=Average of (x in standard units) × (y in standard units)=(1.5)+(1.5)+(0)+(0)+(0.75)+(0.50)+(1.50)7=5.757=0.8214

Thus, the value of r is 0.8214.

The given correlation value (0.7619) and the estimated correlation value (0.8614) both are different. Therefore, no the program is not working correctly.