IQR 20 13 7. - Range = 22, IQR = 20 – 13 = 7. b) See boxplot...

Chapter 1 – Page 1

CHAPTER 1

EXERCISE 1 a) Mean = 17.00, SD = 5.53, median = 17.00, Range = 22,

IQR = 20 – 13 = 7.

b) See boxplot.

c) A typical value for X is 17 which is both the mean and the

median. About half the values are between 13 and 20. The boxplot shows that the upper tail is slightly longer, but difference is small and mean and median are equal. This distribution is roughly symmetric.

(Statistical Methods, 4e Donna Mohr, William Wilson, Rudolf Freund ) (Solution Manual all Chapters) 1 / 4

Chapter 1 – Page 2

EXERCISE 2

Variable Mean Median Variance Standard Deviation Shape WATER 7.125 1.500 452.864 21.28 extremely positively skewed VEG 1.120 0.00 4.327 2.080 extremely positively skewed FOWL 75.635 11.5 42197.33 205.420 extremely positively skewed

WATER Stem Leaf # Boxplot

14 9 1 *

13 12 11 10 9 8 7 6 5 4

3 13 2 *

2

1 05667 5 0

0 00000000000001111111111112222222222345556779 44 +--+--+

----+----+ ----+ ----+ ----+ ----+ ----+ ----+ ----

Multiply Stem.Leaf by 10**+1

VEG

Stem Leaf # Boxplot

9 0 1 *

8

8 0 1 *

7

7 0 1 *

6 6 5

5 2 1 0

4

4 0 1 |

3 |

3 0 1 |

2 8 1 |

2 00002 5 |

1 58 2 +-----+

1 0002 4 | + |

0 58 2 | |

0 00000000000000000000000000000002 32 *-----*

----+----+ ----+ ----+ ----+ ----+ --

• / 4

Chapter 1 – Page 3

FOWL

Stem Leaf # Boxplot

14 1 1 *

13 12 11 10 9 8 7 6 5 4

3 6 1 *

2 124 3 0

1 227888 6 0

0 00000000000000000000001111112222223335678 41 +--+--+

----+----+ ----+ ----+ ----+ ----+ ----+ ----+ -

Multiply Stem.Leaf by 10**+2

b) Frequency distribution for FOWL

Fowl Frequency Midpoint approximate mean = 5500/52

• ≤ x < 100 41 50.0 = 105.8

100 ≤ x < 200 6 150.0 200 ≤ x < 300 3 250.0 approximate variance = 50746 300 ≤ x < 400 1 350.0 1400 ≤ x < 1500 1 1450.0

c) Scatterplots

Aside from the single point with extraordinary number of waterfowl, there is little relationship.

f o wl

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 veg

0 1 2 3 4 5 6 7 8 9 3 / 4

Chapter 1 – Page 4 EXERCISE 3 a)

INDEX:

mean = -0.149 median = -0.155 variance = 1.771 IQR = 1.59 (show stem and leaf, histogram, or boxplot as part of answer)

FUTURE:

mean = -0.208 median = -0.3 variance = 0.601 IQR = 0.81 (show stem and leaf, histogram, or boxplot as part of answer)

b) The Scatter plot is shown below. There is a clear trend for positive changes in the FUTURE contract

value to be associated with positive changes in the NYSE INDEX. Yes, FUTURE can be used to help predict changes in the NYSE index.

index -4 -3 -2 -1

1 2 3 future -3-2-1012

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