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Data Session 5: Solutions
 
Session 5 Part A Part B Part C Part D Part E Homework
 
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Solutions for Session 5, Homework

See solutions for Problems: H1 | H2


Problem H1

First you'll need to find the mean by adding all the values and dividing by 9:

6 + 6 + 9 + 6 + 6 + 7 + 8 + 9 + 6 = 63 / 9 = 7

The mean is 7. (Note that in this calculation, the stacks are not in order. You do not need to order this list before calculating the MAD, variance, or standard deviation.) Here is the table for calculating the MAD:

Number of Coins in Stack (x)

Deviation from the Mean
(x - 7)

Absolute Deviation from the Mean
|x - 7|

6

-1

1

6

-1

1

9

+2

2

6

-1

1

6

-1

1

7

0

0

8

+1

1

9

+2

2

6

-1

1

______

______

______

63

0

10

The MAD is 10 / 9, or approximately 1.11.

Here is the table for calculating the variance:

Number of Coins in Stack (x)

Deviation from the Mean
(x - 7)

Squared Deviation from the Mean
(x - 7)2

6

-1

1

6

-1

1

9

+2

4

6

-1

1

6

-1

1

7

0

0

8

+1

1

9

+2

4

6

-1

1

______

______

______

63

0

14

The variance is 14 / 9, or approximately 1.56.

The standard deviation is the square root of 1.56, which is approximately 1.25. Note that the MAD and the standard deviation are roughly the same.

<< back to Problem H1


 

Problem H2

First you'll need to find the mean by adding all the values and dividing by 9:

1 + 4 + 10 + 4 + 4 + 6 + 7 + 10 + 4 = 50 / 9 = 5.6 (to one decimal place)

We will use 5.6 for the mean. Here is the table for calculating the MAD:

Number of Coins in Stack (x)

Deviation from the Mean
(x - 5.6)

Absolute Deviation from the Mean
|x - 5.6|

1

-4.6

4.6

4

-1.6

1.6

10

+4.4

4.4

4

-1.6

1.6

4

-1.6

1.6

6

+0.4

0.4

7

+1.4

1.4

10

+4.4

4.4

4

-1.6

1.6

______

______

______

50

0

21.6

The MAD is approximately 21.6 / 9 = 2.4 (to one decimal place). (If you are using fractions, the exact answer is 194/81.)

Here is the table for calculating the variance:

Number of Coins in Stack (x)

Deviation from the Mean
(x - 5.6)

Squared Deviation from the Mean
|x - 5.6|2

1

-4.6

21.16

4

-1.6

2.56

10

+4.4

19.36

4

-1.6

2.56

4

-1.6

2.56

6

+0.4

0.16

7

+1.4

1.96

10

+4.4

19.36

4

-1.6

2.56

______

______

______

50

0

72.24

The variance is 72.24 / 9 = 8.0 (to one decimal place). (If you were using fractions, the exact answer is 650/81.)

The standard deviation is the square root of 8, which is 2.8 (to one decimal place). (The exact fractional answer, the square root of 650/81, cannot be expressed by a rational number, since 650 is not a square number.)

The results of Problems H1 and H2 suggest that the data in Problem H2 have greater variation about the mean than the data in Problem H1.

<< back to Problem H2


 

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