Test 1A - Prince George's County Public Schools
Friendly High School
10000 Allentown Road Fort Washington, MD 20744
Office (301)449-4900 Fax (301)449-4911
Raynah Adams
Principal
AP Statistics
Summer Assignments
2013-2014
Summer Assignment 1A AP Statistics Name:
Directions: Work on these sheets. Answer completely, but be concise.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. Which of the following statements is NOT true?
(a) In a symmetric distribution, the mean and the median are equal.
(b) The first quartile is equivalent to the twenty-fifth percentile.
(c) In a symmetric distribution, the median is halfway between the first and third quartiles.
(d) The median is always greater than the mean.
(e) The range is the difference between the largest and the smallest observation in the data set.
2. Consumers’ Union measured the gas mileage in miles per gallon of 38 automobiles from the same model year on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers’ Union. Based on the pie chart, we may conclude that
a) Japanese cars get significantly lower gas mileage than cars of other countries. This is because their slice of the pie is at the bottom of the chart.
b) U.S cars get significantly higher gas mileage than cars from other countries.
c) Swedish cars get gas mileages that are between those of Japanese and U.S. cars.
(d) Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested.
(e) More than half of the cars in the study were from the United States.
[pic]
3. A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct?
a) Your friend must not have followed the diet correctly, since she did not lose weight.
b) Since your friend did not lose weight, the report must not be correct.
c) The report gives only the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend’s experience does not necessarily contradict the study results.
d) In order for the study to be correct, we must now add your friend’s results to those of the study and recompute the new average.
e) Your friend is an outlier.
4. The following is an ogive of the number of ounces of alcohol (one ounce is about 30 milliliters) consumed per week in a sample of 150 college students.
A study wished to classify the students as “light,” “moderate,” “heavy,” and “problem” drinkers by the amount consumed per week. About what percent of students are moderate drinkers, that is, consume between 4 and 8 ounces per week?
a) 60%
b) 20%
c) 40%
d) 80%
e) 50%
5. “Normal” body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5°C with a standard deviation of 0.3°C. When converted to °F, the mean and standard deviation are (°F = °C(1.8) + 32):
a) 97.7, 32
b) 97.7, 0.30
c) 97.7, 0.54
d) 97.7, 0.97
e) 97.7, 1.80
6. The following is a histogram showing the actual frequency of the closing prices of a particular stock on the New York Stock Exchange. The class that contains the 80th percentile is
a) 20–30
b) 10–20
c) 40–50
d) 50–60
e) 30–40
7. Which of the following is likely to have a mean that is smaller than the median?
a) The salaries of all National Football League players.
b) The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores but a few do very poorly.
c) The prices of homes in a large city.
d) The scores of students (out of 100 points) on a very difficult exam in which most get poor scores but a few do very well.
e) Amounts awarded by civil court juries.
8. There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the
a) mean age will stay the same but the variance will increase.
b) mean age will stay the same but the variance will decrease.
c) mean age and variance will stay the same.
d) mean age and variance will increase.
e) mean age and variance will decrease.
9. The weights of the male and female students in a class are summarized in the following boxplots:
Which of the following is NOT correct?
(a) About 50% of the male students have weights between 150 and 185 pounds.
(b) About 25% of female students have weights more than 130 pounds.
(c) The median weight of male students is about 162 pounds.
(d) The mean weight of female students is about 120 pounds because of symmetry.
(e) The male students have less variability than the female students.
10. When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million):
5, 7, 12, bdl, 10, 8, bdl, 20, 6
Which of the following is correct?
(a) The mean lead level in the water is about 10 ppm.
(b) The mean lead level in the water is about 8 ppm.
(c) The median lead level in the water is 7 ppm.
(d) The median lead level in the water is 8 ppm.
(e) Neither the mean nor the median can be computed because some values are unknown.
Part 2: Free Response
Communicate your thinking clearly and completely.
11. The test grades for a certain class were entered into a Minitab worksheet, and then “Descriptive Statistics” were requested. The results were
MTB > Describe 'Grades'.
N MEAN MEDIAN TRMEAN STDEV SEMEAN
Grades 28 74.71 76.00 75.50 12.61 2.38
MIN MAX Q1 Q3
Grades 35.00 94.00 68.00 84.00
You happened to see, on a scrap of paper, that the lowest grades were 35, 57, 59, 60, . . . but you don’t know what the other individual grades are. Nevertheless, a knowledgeable user of statistics can tell a lot about the data set simply by studying the set of descriptive statistics above.
(a) Construct a modified boxplot for these data.
(b) Write a brief description of what the results tell you about the distribution of grades. Be sure to address
• the general shape of the distribution
• unusual features, including possible outliers
• the middle 50% of the data
• any significance in the difference between the mean and the median
12. The University of Miami Hurricanes has been among the more successful teams in college football. The weights in pounds and positions of the players on the 2005 team were recorded. The positions are quarterback (QB), running back (RB), offensive line (OL), wide receiver (WR), tight end (TE), kicker/punter (KP), defensive back (DB), linebacker (LB), and defensive line (DL).
Here are side-by-side boxplots of the weights.
Code: 1=QB, 2=RB, 3=OL, 4=WR, 5=TE, 6=KP, 7=DB, 8=LB, 9=DL
(a) Briefly compare the weight distributions. Which position has the heaviest players overall? Which has the lightest?
(b) Are any individual players outliers within their position?
13. Give an example of a small data set for which the mean is greater than the third quartile. Indicate the mean and the third quartile.
1B AP Statistics Name:
Directions: Work on these sheets. Answer completely, but be concise.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. Mr. Yates picked up a dozen items in the grocery store with a mean cost of $3.25. Then he added an apple pie for $6.50. The new mean for all 13 items is
(a) $3.00
(b) $3.50
(c) $3.75
(d) $4.88
(e) None of the above
Use the following to answer Question 2:
[pic]
2. Which of the following bar graphs is equivalent to the pie chart?
(a) (b)
[pic] [pic]
(c) (d)
[pic] [pic]
(e) None of these.
3. Consider the following ogive of the scores of students in an introductory statistics course:
[pic]
Score
A grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students who obtained a grade of C or C+ is
a) 25%
b) 30%
c) 20%
d) 50%
e) 15%
4. For the following histogram, what is the proper ordering of the mean and median? Note that the graph is NOT numerically precise—only the relative positions are important.
[pic]
(a) I is the mean and II is the median.
(b) II is the median and III is the mean.
(c) I is the median and II is the mean.
(d) II is the mean and III is the median.
(e) I is the mean and III is the median.
5. A researcher wishes to calculate the average height of patients suffering from a particular disease. From patient records, the mean was computed as 156 cm, and standard deviation as 5 cm. Further investigation reveals that the scale was misaligned, and that all readings are 2 cm too large, for example, a patient whose height is really 180 cm was measured as 182 cm. Furthermore, the researcher would like to work with statistics based on meters. The correct mean and standard deviation ar:
a) 1.56m, 0.05m
b) 1.54m, 0.05m
c) 1.56m, 0.03m
d) 1.58m, 0.05m
e) 1.58m, 0.07m
6. A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of women in one of the countries.
Country A: 100, 110, 120, 160, 200
About what percent of Country A women weigh between 110 and 200 pounds?
a) 50%
b) 65%
c) 75%
d) 85%
e) 95%
7. The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is
a) 40 years.
b) 30 years.
c) 25 years.
d) less than 30 years.
e) Cannot be determined from the information given.
8. The time plot below gives the number of burglaries committed each month for a city in Ohio. The plot is for the three-year period January 1987 to December 1989.
[pic]
Which of the following is a true statement?
(a) The number of burglaries in each month of 1988 was lower than the number of burglaries in
each month of 1989.
b) The median number of burglaries for a month in 1988 was a little over 25.
c) The total number of burglaries in 1989 was higher than in 1988.
d) More burglaries seem to be committed in June, July, and August during 1987, 1988, and 1989.
e) None of the above.
9. Here is a summary graph of complex carbohydrates (in grams) for each of three fiber groups in a set of data related to cereals.
Which of the following is NOT correct?
a) The low-fiber group is more variable than the medium-fiber group because the central box is larger.
b) About 25% of low-fiber cereals have less than 12 g of complex carbohydrates per serving.
c) About 50% of medium-fiber cereals have more than 15 g of complex carbohydrates per serving.
d) The average amount of complex carbohydrates per serving for the high-fiber group appears to be much smaller than for the other two groups.
e) About 25% of the medium-fiber cereals have less than 10 g of complex carbohydrates.
10. Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements of nine earthquakes gave the following readings:
4.5 L 5.5 H 8.7 8.9 6.0 H 5.2
where L indicates that the earthquake had an intensity below 4.0 and H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is
(a) Cannot be computed since all of the values are not known
(b) 8.70
(c) 5.75
(d) 6.00
(e) 6.47
Part 2: Free Response
Communicate your thinking clearly and completely.
11. We all “know” that the body temperature of a healthy person is 98.6°F. In reality, the actual body temperature of individuals varies. Here is a back-to-back stemplot of the body temperatures of 130 healthy individuals (65 males and 65 females).
(a) Here are boxplots, produced by Minitab, for these distributions. Label both boxplots with the five-number summary values.
[pic]
(b) Determine whether the 3 points graphed by the + symbol are indeed outliers by our defined criteria.
(c) Write a few sentences comparing the body temperatures of adult males and females.
12. The following data represent scores of 50 students on a calculus test.
72 72 93 70 59 78 74 65 73 80
57 67 72 57 83 76 74 56 68 67
74 76 79 72 61 72 73 76 67 49
71 53 67 65 100 83 69 61 72 68
65 51 75 68 75 66 77 61 64 74
(a) Construct a relative frequency histogram for this data set.
(b) Describe the shape, center, and spread of the distribution of test scores.
(c) Would the mean and standard deviation be appropriate measures of center and spread for these test scores? Explain.
1C AP Statistics Name:
Directions: Work on these sheets. Answer completely, but be concise.
Part I: Multiple Choice. Circle the letter corresponding to the best answer.
1. The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61?
(a) 26
(b) 76
(c) 95
(d) 190
(e) None of these
2. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck.
From this graph we may legitimately conclude that
a) owners of other brands of trucks are less satisfied than the owners of these three brands.
b) Chevrolet owners are substantially more satisfied than Ford or Toyota owners.
c) there is very little difference in the satisfaction of owners for the three brands.
d) Chevrolet probably sells more trucks than Ford or Toyota.
e) a pie chart would have been a better choice for displaying these data.
3. A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players?
a) The mean.
b) The median.
c) Either the mean or median. It doesn’t matter since they will be equal.
d) Neither the mean nor median. Both will be much lower than the actual average salary.
e) The standard deviation should be used to show the great disparity between the astronomical salaries of the few superstars and the salaries of the rest of the players.
4. The mean salary of all female workers is $35,000. The mean salary of all male workers is $41,000. What must be true about the mean salary of all workers?
a) It must be $38,000.
b) It must be larger than the median salary.
c) It could be any number between $35,000 and $41,000.
d) It must be larger than $38,000.
e) It cannot be larger than $40,000.
5. Consider the following output analyzing pH values of some 1986 data on precipitation events.
|[pic] |[pic] |Summary stats for 1986 |
| | |NumNumeric = 55 |
| | |NumNonNumeric = 0 |
| | |NumCases = 55 |
| | |Mean = 6.0673 |
| | |Median = 6.1000 |
| | |Std Deviation = 0.47339 |
| | |Range = 2.4000 |
| | |Minimum = 4.6000 |
| | |Maximum = 7 |
| | |75-th %ile = 6.4000 |
Which of the following is NOT correct?
(a) The 25th percentile is about 5.9.
(b) Some outliers appear to be present below a pH of 5.2.
(c) About 95% of the observations have pH values in the approximate range 6 ± 1.
(d) About 10% of the values are in the range 5.8 to 6.0.
(e) About 75% of the values are less than 6.4.
6. A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as “30” actually had a value of “35.” If we make this correction to the data, then
(a) the mean remains the same, but the median is increased.
(b) the mean and median remain the same.
(c) the median remains the same, but the mean is increased.
(d) the mean and median are both increased.
(e) we do not know how the mean and median are affected without further calculations, but the
variance is increased.
7. Forty students took a statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot:
0|28
1|2245
2|01333358889
3|001356679
4|22444466788
5|000
The third quartile of the score distribution is equal to
(a) 43
(b) 44
(c) 45
(d) 23
(e) 32
8. Rainwater was collected in water collectors at 30 different sites near an industrial comples and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are
(a) 5.64, 1.44 (b) 5.64, 1.32 (c) 5.40, 1.44 (d) 5.40, 1.32 (e) 5.64, 1.20
9. An experiment was conducted to investigate the effect of a new weed killer to suppress weed germination in onion crops. Two chemicals were used, the standard weed killer (C) and the new chemical (W). Both chemicals were tested at high and low concentrations. Measurements are made, of the percent weed germination on each of 50 plots for each treatment combination. Here are some boxplots of the results:
0 10 20 30 40 50
|---------|--------|---------|---------|---------|
|
| _______________
W-low conc. | -----------|________|______|--------
|
| ___________
C-low conc. | ----|_____|_____|----
|
| ______________
W-high conc. | -----|_______|______|---------- * * *
|
| _________
C-high conc. | --|____|____|---
Which of the following is NOT a feature of these data?
(a) At either high or low concentrations, the new chemical (W) gives better control of weed germination than the standard weed killer (C).
(b) Fewer weeds germinate at higher concentrations of both chemicals.
(c) The results from the standard chemical are less variable than those from the new chemical.
(d) High or low concentrations of either chemical have approximately the same effects on weed germination.
(e) Some of the results from the low concentration of weed killer W have fewer weeds germinating than some of the results from the high concentration of W.
10. A clothing and textiles student is trying to assess the effect of a jacket’s design on the time it takes preschool children to put the jacket on. In a pretest, she times 7 children as they put on her prototype jacket. The times (in seconds) are provided below.
n n 65 39 n 43 102
The n’s represent children who had not put the jacket on after 120 seconds (in which case the children were allowed to stop). Which of the following would be the best value to use as the “typical” times required to put on the jacket?
(a) The mean time, which was 62.25 seconds.
(b) The mean time, which was 85.6 seconds.
(c) The median time, which was 54 seconds.
(d) The median time, which was 102 seconds.
(e) The missing times (the n’s) mean we can’t calculate any useful measures of center.
Part 2: Free Response
Communicate your thinking clearly and completely.
11. Ogives of Distributions of Arithmetic Test Scores for Seventh- and Eighth-Graders
(Connect 7s with a smooth curve for seventh-grade ogive and connect 8s with a smooth curve for eighth-grade ogive.)
100+------------------------------------------------7---------8
| | | | | | |
- | | | | 7 | 8 |
| | | | | | |
90+--------|---------|---------|---------|--7------|-----8---|
| | | | | | |
- | | | 7 | |
| | | | | | |
80+--------|---------|---------|-------7-|---------|---8-----|
| | | | | | |
- | | | 7 | | |
| | | | | | |
70+--------|---------|---------|---------|---------|-8-------|
| | | | | | |
- | | | | | |
| | | | | 8 |
PERCENT 60+--------|---------|---------|---------|---------|---------|
| | | | | | |
- | | | | | |
| | | | | | |
50+--------|---------|---------|---------|---------|---------|
| | | | | | |
- | | 7 | 8 | |
| | | | | | |
40+--------|---------|---------|---------|---------|---------|
| | | | | | |
- | | | | | |
| | | | | | |
30+--------|---------|-----7---|---------|--8------|---------|
| | | | | | |
- | | | 8 | |
| | | | | | |
20+--------|---------|-7-------|-------8-|---------|---------|
| | | | | | |
- | 7 | | 8 | | |
| | | | | | |
10+--------|---------|-------8-|---------|---------|---------|
| | | | | | |
- 7 8 | | | |
| | | | | | |
0+----7---|--8------|---------|---------|---------|---------|
5 10 15 20 25 30
TEST SCORE
(a) What is the estimated percent of eighth-grade pupils whose arithmetic scores fall below the median score for grade seven? Justify your answer.
(b) What is the shape of the distribution of the eighth-grade test scores? Justify your answer.
12. During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Here are the data on the number of home runs hit by American and National League teams:
American League 35, 40, 43, 49, 51, 54, 57, 58, 58, 64, 68, 68, 75, 77
National League 29, 31, 42, 46, 47, 48, 48, 53, 55, 55, 55, 63, 63, 67
(a) Construct an appropriate graph for comparing the number of home runs hit in the two leagues.
(b) Calculate numerical summaries of the number of home runs hit in the two leagues. Which of
these numbers would be most appropriate for comparing the two leagues? Explain.
(c) Are there any outliers in either of the two data sets? Justify your answer numerically.
(d) Write a few sentences comparing the distributions of home runs in the two leagues.
1D AP Statistics Name:
Directions: Work on these sheets. Answer completely, but be concise.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. Here are the IQ test scores of 10 randomly chosen fifth-grade students:
145 139 126 122 125 130 96 110 118 118
To make a stemplot of these scores, you would use as stems
(a) 0 and 1.
(b) 09, 10, 11, 12, 13, and 14.
(c) 96, 110, 118, 122, 125, 126, 130, 139, and 145.
(d) 0, 2, 3, 5, 6, 8, 9.
(e) None of the above is a correct answer.
2. For the IQ test scores from the previous question, what kind of plot is appropriate?
(a) a stemplot but not a boxplot
(b) a boxplot but not a histogram
(c) a bar graph but not a pie chart
(d) a histogram but not a dotplot
(e) None of the above is a correct answer.
3. Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following stemplot of the data was constructed.
2|679
3|237789
4|1222446899
5|0556788
6|0233
Which of the following boxplots is correct?
[pic]
4. A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is, a fish that really weighed 26 g was reported to weigh 24 grams. What are the mean and standard deviation after correcting for the error in the scale?
(a) 28 g, 2 g (b) 30 g, 4 g (c) 32 g, 2 g (d) 32 g, 4 g (e) 28 g, 4 g
5. If a distribution is skewed to the right,
(a) the mean is less than the median.
(b) the mean and median are equal.
(c) the mean is greater than the median.
(d) It’s impossible to tell without seeing the data.
(e) None of the above is a correct answer.
6. The population of the United States is aging, though less rapidly than in other developed countries. Here is a stemplot of the percents of residents aged 65 and older in the 50 states, according to the 2000 census:
5 | 7 There are two outliers: Alaska has the lowest percent of older
6 | residents, and Florida has the highest. What is the percent for
7 | Florida?
8 | 5 (a) 13.8%
9 | 679 (b) 57%
10 | 6 (c) 176%
11 | 02233677 (d) 17.6%
12 | 0011113445789 (e) 5.7%
13 | 00012233345568
14 | 034579
15 | 36
16 |
17 | 6
7. Ignoring the outliers, the shape of the distribution in the previous question is
(a) strongly skewed to the right.
(b) slightly skewed to the right.
(c) roughly symmetric.
(d) slightly skewed to the left.
(e) strongly skewed to the left.
8. The center of the distribution in Question 6 is close to
(a) 12.7%.
(b) 13.5%.
(c) 13.8%.
(d) 12.
(e) It’s impossible to tell.
9. To make a boxplot of a distribution, you must know
(a) all of the individual observations.
(b) the mean and the standard deviation.
(c) the quartiles.
(d) the five-number summary.
(e) the individual observations, the mean, and the IQR.
10. What are all the values that a standard deviation can possibly take?
(a) 0 ≤ s (b) 0 ≤ s ≤ 1 (c) –1 ≤ s ≤ 1 (d) s ≤ 0 (e) any real number
Part 2: Free Response
Communicate your thinking clearly and completely.
11. Here are data on the percent of people in several age groups who attended a movie in the past 12 months:
Age group Movie attendance
18 to 24 years 83%
25 to 34 years 73%
35 to 44 years 68%
45 to 54 years 60%
55 to 64 years 47%
65 to 74 years 32%
75 years and over 20%
(a) Display these data in a bar graph in the space above.
What is the main feature of the data?
(b) Would it be correct to make a pie chart of these data? Why?
(c) A movie studio wants to know what percent of the total audience for movies is 18 to 24 years old. Explain why these data do not answer this question.
12. Here is a histogram of the number of unprovoked attacks by alligators on people in Florida over a 33-year period. The classes are “1 ≤ attacks < 3,” “3 ≤ attacks < 5,” and so on.
(a) What is the overall shape of the distribution?
(b) What is the approximate median of the yearly counts of alligator attacks?
(c) Here is a time plot for the alligator data. Connect the numbers from 1 to 8 four times, then 1.
22.5+ 7 5
-
Attacks - 8
- 34 6
- 6
15.0+ 4
- 6 7 2 1 7
-
- 5 2 1
- 81 3
7.5+
- 34 8
- 1 34 7 12 5
- 2 6
- 5 8
0.0+
+-------+-------+-------+-------+-------+
0 8 16 24 32 40
Coded Year (1=1972, 33=2004)
What overall pattern does this plot show?
(d) Why is the typical number of attacks from 1972 to 2004 not very useful in, say, 2006?
13. The states differ greatly in the kinds of severe weather that afflict them. The table below shows the average property damage caused by tornadoes per year over the period from 1950 to 1999 in each of the 50 states and Puerto Rico. (To adjust for the changing buying power of the dollar over time, all damages were restated in 1999 dollars.)
State ($millions) State ($millions) State ($millions)
Alabama 51.88 Louisiana 27.75 Ohio 44.36
Alaska 0.00 Maine 0.53 Oklahoma 81.94
Arizona 3.47 Maryland 2.33 Oregon 5.52
Arkansas 40.96 Mass. 4.42 Penn. 17.11
California 3.68 Michigan 29.88 Puerto Rico 0.05
Colorado 4.62 Minnesota 84.84 Rhode Island 0.05
Connecticut 2.26 Mississippi 43.62 S Carolina 17.19
Delaware 0.27 Missouri 68.93 S Dakota 10.64
Florida 37.32 Montana 2.27 Tennessee 23.47
Georgia 51.68 Nebraska 30.26 Texas 88.60
Hawaii 0.34 Nevada 0.10 Utah 3.57
Idaho 0.26 N Hampshire 0.66 Vermont 0.24
Illinois 62.94 New Jersey 2.94 Virginia 7.42
Indiana 53.13 New Mexico 1.49 Washington 2.37
Iowa 49.51 New York 15.73 W Virginia 2.14
Kansas 49.28 N Carolina 14.90 Wisconsin 31.33
Kentucky 24.84 N Dakota 14.69 Wyoming 1.78
(a) Here is a histogram of the data, with classes “0 ≤ damage < 10,” “10 ≤ damage < 20,” and so on.
Describe the shape, center, and spread of the distribution. Which states may be outliers? (To understand the outliers, note that most tornadoes in largely rural states such as Kansas cause little property damage. Damage to crops is not counted as property damage.)
(b) Here is the “default” histogram that the calculator makes for these data.
How does this calculator histogram compare with the graph in (a)?
[pic]
(c) What are the top five states for tornado damage? The bottom five? (Include Puerto Rico, though it is not a state.)
(d) Give the five-number summary. Explain why you can see from these five numbers that the distribution is strongly skewed to the right.
(e) The histogram suggests that a few states are outliers. Show that there are no suspected outliers according to the 1.5 ( IQR rule. (You see once again that a rule is not a substitute for plotting your data.)
(f) Find the mean property damage. Explain why the mean and median differ so greatly for this distribution.
-----------------------
Percent
Males Females
3 96
96 4
7 96 7
9 96 8
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