2.19)

2.23) a

0 | 1 1 2 3 4 5 5 9

1 | 1 2 3 b. (bold #’s = eclipses)

2 | 0 0 c. Eclipse

3 | 9

4 | 6

5 | 6

6 | 1 5

7 |

8 |

9 |

10| 0

2.36) _

a. The mean of the data is x =å x = 5+4+3+....+0 = 20 =1.429

n 14 14

The median is 1 + 1 = 1 The mode is 0

2

b.Because the mode is the smallest value of the three, the median is the next smallest, and the mean is the largest, the data are skewed to the right. Because the data are skewed, the median is probably a more representative measure for the middle of the data set. Only 5 of the 14 observations are larger than the mean.

c. From the print out, the mean is 55.7 and the median is 36.0. Again, since the mean is larger than the median, the data are skewed to the right. Because the data are skewed, the median is probably a more representative measure for the middle of the data set.

2.38) a. In 1980, the median age of the US pop was 30. This means that half of the people in the US in 1980 were less than 30 and half were older than 30. In 2000, the median age is expected to be 36. This means that half of the people in the US will be less than 36 and half will be older than 36. This means the population as a whole is tending to get older.

b. The shift in the median age to 36 in 2000 will mean that there will be proportionally fewer people in the 18 to 30 age group in 2000 than there was in 1980.

2.39) On average, applicants submitted 2.28 letters of recommendation. Half of the applicants submitted less than 3 letters of recommendation and half submitted 3 or more letters of recommendation.

The number of letters of recommendation submitted most frequently was 3.

2.40)

6 0 000009 b. Median=24

8 1 25 c. Mean=27.82

(2) 2 45 d. Mode=0

7 3 13 e. The mode corresponds to the

5 4 0 smallest number. It doesn’t seem

4 5 to locate the center of the dist.

4 6 2 Both the mean and the median are in

3 7 057 the middle of the stem-&-leaf display. It appears that both of them locate the

center of the data.

2.44) a. gender= qualitative. group= qualitative. DIQ= quantitative. % of pronoun errors=quantitative.

b. Since qualitative numbers do not have meaningful numberassociated with them, you cannot compute numerical measures.

c. DIQ SCORES SLI: mean=93.6; median=91.5; mode=86

d. DIQ SCORES YND: mean=95.3; median=92; mode=92

e. DIQ SCORES OND: mean=101.9; median=103; mode=113.

f. SLI and YND groups appear to be fairly similar with regard to DIQ, while the OND group appears to be much higher. (for all 3)

g. % of pronoun errors: Group(mean, median, mode)=

SLI(30.171, 32.455, 0);YND(46.880, 43.715, 0); OND(0.00, 0.00, 0)

h. yes

2.51)answers will vary

2.56) b. sample 1: range=10; sample 2: range=10

c. s(1)^2=20.9889 s(1)=4.5814; s(2)^2=5.7333 s(2)=2.3944

d. Standard Deviation

2.66)

1975: Interval Freq. Percent

x + s (885.8, 1024.8) 35 70%

x + 2s (816.3, 1094.3) 49 98%

x + 3s (746.8, 1163.8) 50 100%

1990: Interval Freq. Percent

x + s (883.5, 1011.5) 34 68%

x + 2s (819.5, 1075.5) 49 98%

x + 3s (755.5, 1139.5) 50 100%

2.71) a. » 0.025 b. yes

2.72)a. because the data do not follow a mound-shaped distribution, the Empirical Rule wuld not be appropriate.

b. (21,997, 32,237) c. x = 27,117

2.78) pop. mean=60; std dev.=10 2.81)a. z=-3 b. Yes c. No