Homework #2 Solutions:
3.2.	
 a) Not enough information.  The histogram does 
    not provide information about individual ages.  [1]
 b) Same as a).  [31]
 c) 35-44.
 d) 50%.  Approximately 1/2 the area of the histogram 
    corresponds to ages greater than 32.

3.3.
 a) There is rounding error.
 b) No.  The percentages are adjusted for the total numbers 
    of units.  The renter-occupied units may be more frequently 
    occupied by people only needing one room.
 c) Owner-occupied.  

3.5 
 10%.  $10,000 * 1% per $1,000 = 10%.  (see page 37)

3.6 
 (i) and (ii) but not (iii).  In the first two, 25% have 
 heights that round to 67 inches, 50% to 68 inches, and 25% 
 to 69 inches.  In the last, the histogram would have heights 
 of 30%, 40%, and 30% respectively.

3.7
 (i) is natural causes.  Older people are more likely to die 
 of natural causes than young people are.  (ii) is trauma, 
 young people (being naturally reckless) are more likely to 
 die from trauma.

3.9
 a) True.
 b) True.
 c) A 2.0 average is barely passing.  Perhaps many students try 
 to maintain a 2.0 average.  Or, in the self-reports, students 
 who actually had slightly above 2.0 averages rounded their GPAs 
 down to 2.0.

3.12
 False.  The graph plots "Number of riots" by "Temperature", but 
 did not account for differential frequencies of temperatures.  For 
 instance, 85 degree temperatures are markedly more common than 95 
 degree temperatures.  A better graph would 
 plot "Riots/Day" by "Temperature".

4.1
 a) Average = 50.  Standard Deviation = 5.
 b) 48, 50,50. 0.5 standard deviations equals 2.5 units.  

4.2
 a) The second has a smaller standard deviation.  It has all of the 
    observations of the first list, but it also has three additional 
    items at the mean.
 b) The first has the smaller standard deviation.  The second 
    list has the items from the first, along with two very 
    deviant items (99 & 1).

4.3
 a) Around 5.  All the observations are between 0.0 and 10.0.
 b) Around 3.  No observation is greater than 6 units of the mean, 
    so a standard deviation of 6 is not likely.  Very few observations 
    are within 1 unit of the mean, so a standard deviation of 1 is also 
    unlikely.

4.4
 For income, the average would be considerably higher than the mean, 
 since the distribution of income is positively skewed (some people 
 have small incomes, but not less than zero; some people have very 
 large incomes, from hundreds of thousands, to millions, to billions).  
 (pg. 64-65)
 For education, the average would be smaller than the median, as the 
 distribution of education is negatively skewed (pg. 39).

4.6
 a) (i) = 60, (ii) = 50, (iii) = 40.
 b)	(i) median > average.
	(ii) median = average.
	(iii) median < average.
 c) The standard deviation is around 15.  Most, but not nearly all, 
    of the observations are within 15 units of the mean.
 d) False.  The two distributions are nearly symmetrical, so their 
    standard deviations should be equivalent.

4.7
 a) Men: Average = 145 lbs, SD = 20 lbs
    Women: Average = 121 lbs, SD = 20 lbs
 b) 68%.  The two values given are -1 and +1 standard deviation from the mean.
 c) Larger than 9 kg.  Taken together, the distribution of men and women 
    will have more variation than men or women alone.  

4.12
 These data are cross-sectional data; they do not address whether 
 the 12% of people in poverty from one year to another are the same 
 people.  For instance, many people attending college or finding 
 their first job could be considered "in poverty", but they would 
 move out of the poverty ranks with additional experience.

5.1
 a) About 79% of scores should be within 1.25 standard deviations 
    of the mean (pg. A-105).
 b) 1.25 SD * 10 units/SD = 12.5 units.  18 scores are within 
    12.5 units of the mean.
 
5.3
 a) In 1967, a student scoring over 600 would be at least 134 points 
    above the average score.  Divided by the standard deviation 
    (134/110), that score is 1.22 standard deviations above the 
    mean.  Only 11% of scores should be greater than 1.22 standard 
    deviations (pg. A-105).   
 b) 5%.  (same procedure as in 5.3.a)

5.6
 No, they did not follow the normal curve.  In a normal curve, 
 approximately 15% of the scores are more than 1 standard 
 deviation above the mean.  In this sample, no score was more 
 than 1 standard deviation above the mean.

5.7
 a) 7th percentile.  150 point difference = 1.5 standard deviations below 
    the mean.  (pg. A-105).
 b) 570.  

5.8
 a) True.
 b) False.  (The deviations are not affected)
 c) True.
 d) True.  (The deviations are also doubled).
 e) True.
 f) False.  The standard deviation is a squared measure, so changing 
    all the signs does not affect it.

5.10
 40%. Since the distribution is positively skewed, more jobs will 
 be below the average than above the average.  So, the percentage 
 above the average should be less than 50%, probably around 40%.