Homework Chapter 2

2.1.1, 2.1.2, 2.1.3, 2.1.9-10, 2.1.13, 2.1.20

Section 2.1

Question 1

data:

[1] 0 5 1 1 3

$mean
[1] 2

$median
[1] 1

$mode
[1] 1

Question 2

data:

[1] 3 2 5 6 4 4 3 5

$mean
[1] 4

$median
[1] 4

$mode
[1] 3 4 5

Question 3

data:

 [1]  3  5  4  5 10  5  6  9  2  8

$mean
[1] 5.7

$median
[1] 5

$mode
[1] 5

Question 9-10

Q9

$mean
[1] 3.929167

$median
[1] 3.9

Q10

The mean and median are very similar suggesting that the distribution is symmetric.

Q13

$mean
[1] 0.8959286

$median
[1] 0.68

Data appears to be skewed right (mean > median)

Q20

The median is recommended because we assume the salaries come from a very skewed distribution (right skewed).

Section 2.2 and 2.3

2.2.1, 2.2.3, 2.2.10, 2.3.26

2.2.1

[1] 2 1 1 3 5

Variance: 2.8

Standard Deviation: 1.67

2.2.3

[1] 3 1 5 6 4 4 3 5

Variance: 2.41

Standard Deviation: 1.55

2.2.10

[1] 1.28 2.39 1.50 1.88 1.51

a

Range:

b

Variance

[1] 0.19

Standard Deviation

[1] 0.44

c

Range/Standard Deviation =

[1] 2.5

The range is about 2.5 more than the standard deviation. This less than the 4x we saw in the range/sd approximation.

2.3.26

a

b

Mean

[1] 7.73

c

Standard Deviation

[1] 1.98

Calculations are below - compare to the values for Tchebysheff’s and Empircal rule that are given in text:

multiplier	lower_interval	upper_interval	actual_contained
1	5.75	9.71	71%
2	3.77	11.69	96%
3	1.79	13.67	100%