AP Review Questions 61-120 Flashcards
Find the mean and median from the datasets below. Which measure of central tendency would be the appropriate measure to use for each? Why? Dataset 1: {7,7,2,8,5,10,9,1,10,3} Dataset 2: {6,2,6,5,3,8,5,7,15,5,} (A) Dataset 1 and 2: mean: 6.2; because there are no outliers. (B) Dataset 1: Mean: 6.2; because there are no outliers. Dataset 2: Median: 5.5; because 15 is an outlier. (C) Dataset 1: Median: 7; because there are no outliers. Dataset 2: Mean: 6.2; because 15 is an outlier. (D) Datasets 1 and 2: Median: 6.2; because 10 and 15 are outliers. (E) Datasets 1 and 2: Mean: 6.2; because 10 and 15 are outliers.
(B) The interquartile ranges for the datasets are 6 and 2, respectively. There are no outliers in Dataset 1 so the mean of 6.2 would be the best measure of central tendency. 15 is an extreme outlier in Dataset 2, so the median 5.5 would be the best measure of central tendency since the mean is more sensitive to outlier.
A score at or above the 90th percentile is how many standard deviations from the mean? (A) 1.28 standard deviations or more above the mean. (B) 1.64 standard deviations or more above the mean. (C) 2.58 standard deviations or more above the mean. (D) 1.28 standard deviations or more below the mean. (E) 1.64 standard deviations or more below the mean.
(A) The z-score with area of 0.9 to the left of it is 1.28 which means that the 90th percentile or above is 1.28 standard deviations above the mean.
A score at or above the 70th percentile is how many standard deviations form the mean? (A) 0.52 standard deviations or more above the mean. (B) 1.04 standard deviations or more above the mean. (C) 1.64 standard deviations or more above the mean. (D) 0.52 standard deviations or more below the mean. (E) 1.04 standard deviations or more below the mean.
(A) The z-score with area of 0.7 to the left of it is 0.52 with means that the 70th percentile or above is 0.52 standard deviations above the mean.
Test scores are normally distributed with a mean of 72 and a standard deviation of 4.2. What is the percentile of a score of 65 (round to the nearest whole percentile). (A) 95th percentile (B) 90th percentile (C) 85th percentile (D) 5th percentile (E) 1st percentile
(D) The z-score associated with a test score of 65 is 65-72/4.2=-1.67. The area to the left of a z-score of -1.67 is 0.0475 or approximately the 5th percentile.
What data point is indicated on the distribution. With a mean of 67.0 and a standard deviation of 5.1. (A) 61.9 (B) 64.5 (C) 67.0 (D) 72.1 (E) 77.2
(D) The data point is at the point of inflection on the bell curve which is one standard deviation above the mean or X=67+5.1=72.1.
The wage gap between men and women’s earnings was 23 cents on the dollar in 2009, down from a low of 22.2 cents in 2007. Some regions in the Untied States are more progressive and pay is more equitable between genders. “According to WebMD, male specialists earn a median salary of $225,000 a year. Female specialists, on the other hand, take home a median annual salary o f$160,000– a difference of $65,000 a year. This difference in pay means that in the course of a 35-year career, female doctors lose a total of $2.3 million on average, noted Forbes.” (a) What might explain the reporting of median salaries rather than average salaries? (b) A sample of eight specialist salaries for male and female doctors was collected in one region of the United States. A summary is shown. On average, how does this sample compare with findings by WebMD? How does it compare to the wage gap reported for 2009 of 23 cents on the dollar? Men Women Category Mean Median Mean Median Anesthesiologist 267.9 247 189.3 194 Obstetricians/ 158.8 148 143.7 143 Gynecologists pediatricians 141.4 146 112.8 112 psychiatrists 157.4 171 114.1 126 surgeons 196 200 149.1 164 podiatrists 97.8 89 74.3 74
(a) If there are outliers, particularly extreme outliers, the median is less sensitive and more resistant than the mean. That may explain why median salaries would be reported rather than average salaries (b) From the summary data, extracting the specialist and finding the median shows that, for men, it is 148+171/2=159.5. For women, it is 143+126/2=134.5. This is lower than what was reported; additionally, the wage gap for these two medians is about 16 cents, which is less than the reported 23 cents for 2009. 159.5-134.5/159.5=X/100, x=16.
Researchers form the University of Pennsylvania, Philadelphia, found that incentives increased all IQ scores, but particularly for those of individuals with lower baseline IQ scores. They found that a financial incentive could raise IQ as much as 15 points. (a) Construct a graphical display for each variable shown in the following dataset. Boys IQ Scores No Incentive Incentive 108 105 89 132 93 116 94 81 115 83 96 90 73 85 85 131 103 136 (b) Analyze the data for outliers (c) Report an appropriate measure of central tendency for both groups. (d) what is the IQ score for the 75th percentile for both samples?
(a) Stem- and- leaf of No Incentive N=10 Leaf Unit= 10 1 7 3 3 8 59 (3) 9 346 4 10 38 2 11 5 1 12 3 stem- and-leaf of incentive N=10 Leaf Units= 1.0 4 8 0259 5 9 0 5 10 4 4 11 6 3 12 3 13 125 (b) The stem and leaf plots indicate that the neither group has any outliers. There are no data points in either group that are more than 1.5(IQR) above Q3 or more than 1.5(IQR) below Q1. (c) The mean would be an
h
Water consumption in gallons per day from a small town is listed below.
water consumed
167, 180, 192, 173, 145, 151, 174, 175, 178, 160, 195, 224, 244, 146, 162, 146, 177, 163, 149, 188
(a) construct a frequency distribution table using only five classes.
(b) construct a graphical display.
(c) report an appropriate measure of central tendency.
(d) analyze the data for outliers using a box plot.
(A) classes Frequency
- 5-165 8
- 5-186 7
- 5-207 3
- 5-228 1
- 5-249 1
20
(b)
- 5669
- 1
- 0237
(5) . 17. 34578
- 0237
- 08
- 25
- 20
- 21
- 4
- 23
- 4
(C) due to the outlier, the median– 173.5 gallons per day– would be an appropriate measure of central tendency.
The following is a sample of butterfly wingspan measured in millimeters.
wingspand
32,31,29,46,37,38,40,30,28,33,36,39,37,39,41,29,32,38,39,35,37,33
(a) construct a steam and leaf plot.
(b) reporte an appropriate measure of central tendency.
(c) analyze the data for outliers.
(d) what wingspan is the 75th percentile.
(A)
- 2899
- 3012233
(10) . 35677788999 - 401
- 46
(b) with the absence of outliers, the mean– 35.4 mm– is an appropriate measure of central tendency. The median– 36.5 mm– is also an appropriate measure of central tendency.
(C) the box plot indicates that there are no outliers. There are no date points in either group that are more than 1.5(iqr) above q3 or more than 1.5(iqr) below q1.
(d) the third quartile is the same as the 75th percentile. 39 is the wingspan for the 75th percentile.
Which of the following statements best describes the scatter plot, that has a positive correlation and association.
I. A linear model would fit the data well.
II. The bivariate data are positive correlated.
III. the linear relationship is weak.
(a) I only
(b) I and III only
(c) I and II only
(d) II ONLY
(e) III only
(C) the data points are trending linearly with a positive slope.
What can be said about the relationship between time spent studying and test scores? Based on a positive correlation and association, scatter plot.
(a) more time spent studying is related to lower test scores.
(b) less time spent studying is related to higher test scores.
(c) more time spent studying is related to higher test scores.
(d) higher test scores are caused by more time spent studying.
(e) there is no discernible relationship between study time and test scores.
(C) the more time spent studying is related to a higher test scores since there is a positive relationship.
(B) y = 24.765+ 9.051x. There is positive linear correlation.
From the data, find the least-squares regression line. What type of correlation is there?
study(hrs). Test scores
- 20
- 35
- 50
- 47.5
- 65
- 72.5
- 75
- 67.5
- 92.5
- 85
- 90
- 95
- 70
(a) y = 24.765-9.051x. There is negative linear correlation.
(b) y = 24.765+9.051x. There is positive linear correlation.
(c) y = 9.051+24.765x. There is positive linear correlation.
(d) y = 9.051-24.765x. There is negative linear correlation.
(e) y = -24.765+9.051x. There is negative linear correlation.
(D) y = 95.494-4.508x. There is negative linear correlation.
From the data, find the least-squares regression line. What type of correlation is there?
entertainment media. Test scores
- 97.5
- 85
- 82.5
- 75
- 95
- 67.5
5 75
5 82.5
6 57.5
7 65
7 75
10 45
(a) y = 95.494+4.508x. There is positive linear correlation.
(b) y = 4.508-95.494x. There is negative linear correlation.
(c) y = 4.508+95.494x. There is negative linear correlation.
(d) y = 95.494-4.508x. There is negative linear correlation.
(e) y = -95.494-4.508x. There is negative linear correlation.
d
d