Answer Key Problem set 3

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APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I 1. #3.10 b) 11+6+20+9+13+4+39+13+44+7/10=16.6 mean= 16.6, (11-16.6)^2+ (6-16.6)^2+(20-16.6)^2+ (9-16.6)+ (13-16.6)^2+ (4-16.6)^(39-16.6)^2+(13- 16.6)^+(44-16.6)^2+(7-16.6)^2= 193.6 s  13.91 c) New study length of stay= 32, 18, 55, 17, 24, 31, 20, 40, 24, 15 Mean= 32+18+55+17+24+31+20+40+24+15=27.6 (32-27.6)^2+(18-27.6)^2+(55-27.6)^2+(17-27.6)^2+(24-27.6)^2+(31-27.6)^2+(20-27.6)^2+(40- 27.6)^2+(24-27.6)^2+(15-27.6)^2=153.6 s  12.39 25 years ago, the data set had a mean of 27.6 and a standard deviation of 11.76. The current study has a mean of 16.6 with a standard deviation of 13.91. In 25 years, the mean decreased by 11 days and the standard deviation decreased by 1.52. d) We can’t calculate the mean, but substituting 40 would give a mean of the censured observation 18.7 days. The new median would be the result of 11 observations with a new median of 13 days. 2. #3.26 10 is a realistic estimate because -20 is impossible (since standard deviation can’t be negative), a score of 0 would mean that everyone scored a 76 on the exam and 50 seems too large for the possible range of scores. Students did worse on the exam, so 10 is realistic. #3.42 a) The range of the dataset is 92.3-78.3=14 and the IQR is 88.8—83.6=5.2. b) Lower outliers would be observations that are less than Q1 -1.5 (IQR)=83.6-1.5 (5.2)=75.8 and higher outliers would be observations greater than Q3+1.5(IQR)= 88.8+1.5(5.2)= 96.6. There are no outliers that lie lower than 75.8 or higher than 96.6.

APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I # 3.78 a) The new mean is 77 and the new standard deviation is still 20. b) The new mean is $200,000 and the new standard deviation is $60,000 c) In order to get the new mean, the original mean will need to be multiplied by 1.6 and the standard deviation is multiplied by 1.6. 3. a) . tabstat wage, stat (min, p25, p50, p75, max, iqr) variable | min p25 p50 p75 max iqr -------------+------------------------------------------------------------ wage | 115 668 905 1160 3078 492 -------------------------------------------------------------------------- . tabstat wage if educ==16, stat(min, p25, p50, p75, max, iqr) variable | min p25 p50 p75 max iqr -------------+------------------------------------------------------------ wage | 233 827 1049.5 1346 2137 519 . tabstat wage if educ==12, stat (min, p25, p50, p75, max, iqr) variable | min p25 p50 p75 max iqr -------------+------------------------------------------------------------ wage | 115 635 840 1040 2500 405 -------------------------------------------------------------------------- b) The IQR for those with an education of 16 years (519), is larger than 12 years of education (405).

APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I c) The boxplot shows the minimum (1), 25 th percentile (8), Median or 50 th percentile (11), 75 th percentile (15), and the maximum (25). The whiskers extend to the minimum and maximum inputs of the variable if there are no outliers present. In this boxplot, no outliers exist. d) e) The median IQ is lower for those who have between 13 and 15 years of education and begins to increase for those who have 16 years or more of education. Outliers are present in years of education from 13-17, which effect the distribution of the data. The observation at 18 years is the only one without any outliers. None of the observations are symmetric, since each observation either has outliers, or has higher values in either the lower or upper half of the boxplot.

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APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I f) When adjusting the monthly earnings, multiplication would be stretching the data. This affects the spread and location of the distribution of data, so the mean and standard deviation of the data. The shape and symmetry would remain the same, however. g) The new variable (which I called wagenew) has a lower mean, median and standard deviation than wage, but both variables have the same standard deviation. The mean and the standard deviation for iq are standardized. The scores seem to increase in increments of ten, with a defined minimum and maximum.

APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I h) The scores appear to be standardized. From the histogram, the mean is around 101, with a standard deviation of about 15. When looking at the histogram, values to the left of the median and values to the right appear symmetrical. There are few outliers in this dataset. i.)

APSTA.GE.2001—Statistics for the Behavioral and Social Sciences I Problem Set I j.) The percent of men who have a very high IQ is 444/935 or ~0.475%. 26.80% of men completed college. The z score of 1.75 corresponds to the 75 th percentile or a score range above 112.

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