CHAPTER 2

SUMMARIZING DATA

2-2.

As the table shows, the trimmed mean changes least as a percentage of its original value, so could be regarded as most resistant.

With Sun Without Sun Difference % Difference

$$\bar{y} = 179717.7 \bar{y} = 44846.4$$ 134871.3 300.7

$$Q_2 = \displaystyle\frac{12756+49528}{2} = 31142$$ Q₂ = 12756 18386 144.1

$$\bar{y}_{t1} = 50166 \bar{y}_{t1} = 36932.6$$ 13233.4 35.8

2-3.

The data are in two distinct groups: 2,3,4,5 years and 12,13,15,15,18,20 years.
The first has mean 3.5 years, standard deviation 1.29 years.
The second has mean 15.5 and standard deviation 3.02 years.
The first were sentenced by ``letemgo", the second by ``lockemup".

2-5.

Process Q₁ Q₂ Q₃ IQR

1 .15 .22 .43 .28

2 .02 .04 .09 .07

Process 1 - Higher but more variable yields.

Process 2 - Lower but more consistent yields

2-10.

80;0.15

2-18.

His quote would imply that the see-saw could be balanced by putting all the weight on one side of the fulcrum.

2-20.

The value 20 is an outlier.

 

Figure 1:   Boxplot for Exercise 2-20

2-24.

Skewed right, unimodal. Mode at $\approx 16\;\;\;Q_1 = 12.2,\;\;Q_2 = 17.7\;\;Q_3 = 23.3$.

2-27.

1/4 of the mileages are below Q₁ = 63,500

1/2 of the mileages are below Q₂ = 88,000

3/4 of the mileages are below Q-3 = 149,000

The average mileage is 94,778.

 

Figure 2:   Boxplot for Exercise 2-27