Chapter 1: Looking at Data—Distributions - PowerPoint Presentation

Slide1

Chapter 1:Looking at Data—Distributions

© 2017 W.H. Freeman and CompanySlide2

1.1-1When ordering vinyl replacement windows, the following variables are specified for each window. Which of these variables is quantitative?a. window style: double hung, casement, or awning

b. area of the window opening in square inchesc. window style: single pane or double pane1.1 DataSlide3

1.1-1 answerWhen ordering vinyl replacement windows, the following variables are specified for each window. Which of these variables is quantitative?a. window style: double hung, casement, or awning

b. area of the window opening in square inches (correct)c. window style: single pane or double pane1.1 DataSlide4

1.1-2A survey of college students collected information on several variables: distance from home, age, major, gender, and class. The variable major isa. quantitative.

b. categorical.c. neither categorical nor numeric.1.1 DataSlide5

1.1-2 answerA survey of college students collected information on several variables: distance from home, age, major, gender, and class. The variable major isa. quantitative.

b. categorical. (correct)c. neither categorical nor numeric.1.1 DataSlide6

1.1-3On a job application, there are a number of questions: - What is your Social Security number? - What is your address? - What is your phone number?

Which of the above variables are NOT categorical?a. Social Security numberb. address

c. phone number

d. none, they are all categorical variables

1.1 DataSlide7

1.1-3 answerOn a job application, there are a number of questions: - What is your Social Security number? - What is your address? - What is your phone number?

Which of the above variables are NOT categorical?a. Social Security numberb. address

c. phone number

d. none, they are all categorical variables (correct)

1.1 DataSlide8

1.1-4An eager statistics student wanted to help his boss. He studied the data on products sold at the store over a period of a week and reported to the boss that the average UPC number was 1001264789 with a standard deviation of 45378. From this information, his boss shoulda. make sure there are a lot of 1001264789 items on hand.b. know that approximately 68% of all items had UPC codes between 1001219411 and 1001310167.

c. do nothing; the statistics reported are invalid.1.1 DataSlide9

1.1-4 answerAn eager statistics student wanted to help his boss. He studied the data on products sold at the store over a period of a week and reported to the boss that the average UPC number was 1001264789 with a standard deviation of 45378. From this information, his boss shoulda. make sure there are a lot of 1001264789 items on hand.b. know that approximately 68% of all items had UPC codes between 1001219411 and 1001310167.

c. do nothing; the statistics reported are invalid. (correct)1.1 DataSlide10

1.1-5Which value leaves 25% of the data above it?a.

b. medianc.

1.1 DataSlide11

1.1-5 answerWhich value leaves 25% of the data above it?a.

(correct)b. medianc.

1.1 DataSlide12

1.2-1A sample of 160 workers in the downtown area classified each worker by race. A bar graph of the results is given below, but the bar for blacks in the graph below has been omitted.Using the information provided, the proportion of black workers in the sample must be

a. 40%.b. 25%.c. 20%.

?

80

60

40

20

0

1.2 Displaying Distributions with GraphsSlide13

1.2-1 answerA sample of 160 workers in the downtown area classified each worker by race. A bar graph of the results is given below, but the bar for blacks in the graph below has been omitted.Using the information provided, the proportion of black workers in the sample must be

a. 40%.b. 25%. (correct)c. 20%.

?

80

60

40

20

0

1.2 Displaying Distributions with GraphsSlide14

1.2-2The professor of a large statistics class decided to take a survey of what models of cars her students drive. In this class of 100, what is the percentage of students who drive a Ford?a. 40%b. 45%

c. 50%

1.2 Displaying Distributions with GraphsSlide15

1.2-2 answerThe professor of a large statistics class decided to take a survey of what models of cars her students drive. In this class of 100, what is the percentage of students who drive a Ford?a. 40%b. 45% (correct)

c. 50%

1.2 Displaying Distributions with GraphsSlide16

1.2-3The professor of a large statistics class decided to take a survey of what models of cars her students drive. The results are illustrated below. What type of display is this?a. bar graphb. histogram

c. stemplot

1.2 Displaying Distributions with GraphsSlide17

1.2-3 answerThe professor of a large statistics class decided to take a survey of what models of cars her students drive. The results are illustrated below. What type of display is this?a. bar graph (correct)b. histogram

c. stemplot

1.2 Displaying Distributions with GraphsSlide18

1.2-4The time plot below is for motor vehicle deaths in the United States. The rate is the number of deaths per million miles driven and is plotted for the 18 years: 1960, 1962, 1964, ...,

1992, 1994. Suppose we drew a histogram of these 18 death rates using class intervals 1–1.9,

2–2.9

,

3–3.9

,

4–4.9

,

and

5–5.9

.

Using the histogram, we would

a. lose all information about

trends over time.

b. be able to compute the

number of years in this period

for which the death rate was 5

or higher.

c. both of the above.

1.2 Displaying Distributions with GraphsSlide19

1.2-4 answerThe time plot below is for motor vehicle deaths in the United States. The rate is the number of deaths per million miles driven and is plotted for the 18 years: 1960, 1962, 1964, ...,

1992, 1994. Suppose we drew a histogram of these 18 death rates using class intervals 1–1.9,

2–2.9

,

3–3.9

,

4–4.9

,

and

5–5.9

.

Using the histogram, we would

a. lose all information about

trends over time.

b. be able to compute the

number of years in this period

for which the death rate was 5

or higher.

c. both of the above. (correct)

1.2 Displaying Distributions with GraphsSlide20

1.2-5High levels of glucose in the blood are indications of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications, such as blindness and heart disease. A random sample of 180 individuals had their blood sugar level measured. The results are displayed in the graph. The shape of the distribution of blood glucose levels is

a. unimodal, left-skewed.b. bimodal.c. unimodal

, right-skewed.

Blood glucose

1.2 Displaying Distributions with GraphsSlide21

1.2-5 answerHigh levels of glucose in the blood are indications of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications, such as blindness and heart disease. A random sample of 180 individuals had their blood sugar level measured. The results are displayed in the graph. The shape of the distribution of blood glucose levels is

a. unimodal, left-skewed.b. bimodal.c. unimodal

, right-skewed.

(correct)

Blood glucose

1.2 Displaying Distributions with GraphsSlide22

1.2-6Test scores for a class of 40 students are displayed in the histogram below, a grade of 60 or higher is required to pass the test. What percentage of students passed the test?a. 55%

b. 60%c. 65%d. 70%e. 75%

1.2 Displaying Distributions with GraphsSlide23

1.2-6 answerTest scores for a class of 40 students are displayed in the histogram below, a grade of 60 or higher is required to pass the test. What percentage of students passed the test?a. 55%

b. 60%c. 65% (correct)d. 70%e. 75%

(5+9+7+5)/40 = 26/40 = 0.65

1.2 Displaying Distributions with GraphsSlide24

1.3-1Consider the following stemplot. The mean of the data represented in this stemplot

a. is 34.5.

b

. is 37.

c

. cannot be computed from the information.

1.3 Describing Distributions with NumbersSlide25

1.3-1 answerConsider the following stemplot. The mean of the data represented in this stemplot

a. is 34.5.

b

. is 37

. (correct)

c

. cannot be computed from the information.

1.3 Describing Distributions with NumbersSlide26

1.3-2Consider the following stemplot. The median of the data represented in this stemplot

a. is 30.5.

b

. is 34.5.

c

. cannot be computed from the information given.

.

1.3 Describing Distributions with NumbersSlide27

1.3-2 answerConsider the following stemplot. The median of the data represented in this stemplot

a. is 30.5.

b

. is 34.5

. (correct)

c

. cannot be computed from the information given.

.

1.3 Describing Distributions with NumbersSlide28

1.3-3A sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year.33 31 24 36The variance of their salaries is

a. 5.1.b. 26.c. 31.

1.3 Describing Distributions with NumbersSlide29

1.3-3 answerA sample was taken of the salaries of four employees from a large company. The following are their salaries (in thousands of dollars) for this year.33 31 24 36The variance of their salaries is

a. 5.1.b. 26. (correct)c. 31.

1.3 Describing Distributions with NumbersSlide30

1.3-4The average GPA of 40 students in a statistics class is 3.46, while the average GPA of the 32 students in the calculus class across the hall is 3.58. Two students from the calculus class, both with a GPA of 3.71, decide to drop the course and enter into the statistics class. What are the new average GPAs of the statistics and calculus classes, respectively?a. 3.63 and 3.84b. 3.59 and 3.71

c. 3.47 and 3.571.3 Describing Distributions with NumbersSlide31

1.3-4 answerThe average GPA of 40 students in a statistics class is 3.46, while the average GPA of the 32 students in the calculus class across the hall is 3.58. Two students from the calculus class, both with a GPA of 3.71, decide to drop the course and enter into the statistics class. What are the new average GPAs of the statistics and calculus classes, respectively?a. 3.63 and 3.84b. 3.59 and 3.71

c. 3.47 and 3.57 (correct)

1.3 Describing Distributions with NumbersSlide32

1.3-5The scores on the Survey of Study Habits and Attitudes (SSHA) for a sample of 150 first-year college women produced the following boxplot and descriptive statistics using MINITAB. The number of women with scores between 93.26 and 129.23 is

Descriptive Statistics

Variable N Median Min

SSHA

150 110.68 42.49

Max Q1 Q3__

182.71 93.26 129.23

a. about 75.

b. about 50.

c. about 36.

1.3 Describing Distributions with NumbersSlide33

1.3-5 answerThe scores on the Survey of Study Habits and Attitudes (SSHA) for a sample of 150 first-year college women produced the following boxplot and descriptive statistics using MINITAB. The number of women with scores between 93.26 and 129.23 is

Descriptive Statistics

Variable N Median Min

SSHA

150 110.68 42.49

Max Q1 Q3__

182.71 93.26 129.23

a. about 75

. (correct)

b. about 50.

c. about 36.

1.3 Describing Distributions with NumbersSlide34

1.3-6A sample was taken of the salaries of 20 employees from a large company. The following are the salaries (in thousands of dollars) for this year (the data are ordered).

28

31

34

35

37

41

42

42

42

47

49

51

52

52

60

61

67

72

75

77

Suppose each employee in the company receives a $3000 raise for next year (each employee’s salary is increased by $3000). The interquartile range (

IQR

) of the salaries will

a. be unchanged.

b

. increase by $3000.

c

. be multiplied by $3000.

1.3 Describing Distributions with NumbersSlide35

1.3-6 answerA sample was taken of the salaries of 20 employees from a large company. The following are the salaries (in thousands of dollars) for this year (the data are ordered).

28

31

34

35

37

41

42

42

42

47

49

51

52

52

60

61

67

72

75

77

Suppose each employee in the company receives a $3000 raise for next year (each employee’s salary is increased by $3000). The interquartile range (

IQR

) of the salaries will

a. be unchanged

. (correct)

b

. increase by $3000.

c

. be multiplied by $3000.

1.3 Describing Distributions with NumbersSlide36

1.3-7A distribution has a mean of 100 and a median of 120. The shape of this distribution is most likelya. skewed left.b. skewed right.c. symmetric.

1.3 Describing Distributions with NumbersSlide37

1.3-7 answerA distribution has a mean of 100 and a median of 120. The shape of this distribution is most likelya. skewed left. (correct)b. skewed right.

c. symmetric. 1.3 Describing Distributions with NumbersSlide38

1.3-8Which of the following measures is least affected by outliers?a. the meanb. the standard deviationc. the

IQR1.3 Describing Distributions with NumbersSlide39

1.3-8 answerWhich of the following measures is least affected by outliers?a. the meanb. the standard deviation

c. the IQR (correct)1.3 Describing Distributions with NumbersSlide40

1.3-9A couple just gave birth to sextuplets. What will be the standard deviation of their ages 10 years from now?a. 1.7 yearsb. 10 years

c. 0 years1.3 Describing Distributions with NumbersSlide41

1.3-9 answerA couple just gave birth to sextuplets. What will be the standard deviation of their ages 10 years from now?a. 1.7 yearsb. 10 years

c. 0 years (correct) 1.3 Describing Distributions with NumbersSlide42

1.3-10Does the value of the standard deviation depend on the value of the mean?a. Yes. If the mean gets larger, the standard deviation will also get larger.b. Yes. You need to know the mean to be able to calculate the standard deviation.

c. No. The center of a distribution and the spread are not related.1.3 Describing Distributions with NumbersSlide43

1.3-10 answerDoes the value of the standard deviation depend on the value of the mean?a. Yes. If the mean gets larger, the standard deviation will also get larger.b. Yes. You need to know the mean to be able to calculate the standard deviation

. (correct)c. No. The center of a distribution and the spread are not related.

1.3 Describing Distributions with NumbersSlide44

1.3-11A teacher gave a 25-question multiple-choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this informationa. all the students had the same score.

b. she must have made a mistake.c. about half the scores were above the mean.1.3 Describing Distributions with NumbersSlide45

1.3-11 answerA teacher gave a 25-question multiple-choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this informationa. all the students had the same score. (correct)

b. she must have made a mistake.c. about half the scores were above the mean.

1.3 Describing Distributions with NumbersSlide46

1.3-12The five-number summary of scores on a test is:35 60 65 70 90Based on this information

a. there are no outliers.b. there are low outliers.c. there are both high and low outliers.

1.3 Describing Distributions with NumbersSlide47

1.3-12 answerThe five-number summary of scores on a test is:35 60 65 70 90Based

on this informationa. there are no outliers.b. there are low outliers.c. there are both high and low outliers.

(correct

)

1.5 (

IQR

) = 15

-15

15

1.3 Describing Distributions with NumbersSlide48

1.3-13The following is a sample of the weights of 12 boxers from various weight classes:121 173 157 165 170 161 142 171 184 100 145 196What is the median value of this data set?

a. 151.5b. 163c. 157.1

1.3 Describing Distributions with NumbersSlide49

1.3-13 answerThe following is a sample of the weights of 12 boxers from various weight classes:121 173 157 165 170 161 142 171 184 100 145 196What is the median value of this data set?

a. 151.5b. 163 (correct)c. 157.1

Order data and median is an average of 161 and 165.

1.3 Describing Distributions with NumbersSlide50

1.3-14The following is a sample of the weights of 12 boxers from various weight classes: 121 173 157 165 170 161 142 171 184 100 145 196How many values are going to be considered outliers?

a. 0b. 1c. 2

1.3 Describing Distributions with NumbersSlide51

1.3-14 answerThe following is a sample of the weights of 12 boxers from various weight classes: 121 173 157 165 170 161 142 171 184 100 145 196How many values are going to be considered outliers?

a. 0b. 1 (correct)c. 2

IQR

= 28.5, LF = 143.5 – (1.5)(28.5) = 100.75

UF = 172 + (1.5)(28.5) = 214.75

1.3 Describing Distributions with NumbersSlide52

1.3-15The NHL consists of 24 teams from the United States and six teams from Canada. The mean number of goals per game for the NHL was 2.74. What was the total number of goals for the NHL?a. 3.25

b. 3.30c. 3.43d. 3.56e. 3.98

1.3 Describing Distributions with NumbersSlide53

1.3-15 answerThe NHL consists of 24 teams from the United States and six teams from Canada. The mean number of goals per game for the NHL was 2.74. What was the total number of goals for the NHL? a. 3.25

b. 3.30c. 3.43 (correct)d. 3.56e. 3.98

1.3 Describing Distributions with NumbersSlide54

1.3-16A father drops his three children off at the movie theater and gives them each $25 to spend on a movie and concession snacks. After each of the children buys a movie ticket for $9, what is the standard deviation of the amount of money the children have left? a. $3

b. $2.12c. $4d. $2.83e. $0

1.3 Describing Distributions with NumbersSlide55

1.3-16 answerA father drops his three children off at the movie theater and gives them each $25 to spend on a movie and concession snacks. After each of the children buys a movie ticket for $9, what is the standard deviation of the amount of money the children have left? a. $3

b. $2.12c. $4d. $2.83e. $0 (correct)

1.3 Describing Distributions with NumbersSlide56

1.4-1The time for students to complete a standardized placement exam given to college freshman has a Normal distribution with a mean of 62 minutes and a standard deviation of 8 minutes. If students are given 1 hour to complete the exam, the proportion of students who will complete the exam is abouta. 0.25.b. 0.40.

c. 0.60.1.4 Density Curves and Normal DistributionsSlide57

1.4-1 answerThe time for students to complete a standardized placement exam given to college freshman has a Normal distribution with a mean of 62 minutes and a standard deviation of 8 minutes. If students are given 1 hour to complete the exam, the proportion of students who will complete the exam is abouta. 0.25.b. 0.40. (correct)

c. 0.60.

P

(

z < -0.25)

1.4 Density Curves and Normal DistributionsSlide58

1.4-2The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the top 10% of students are given an A, what is the lowest mark a student can have and still be awarded an A?a. 63.28b. 70.97

c. 76.081.4 Density Curves and Normal DistributionsSlide59

1.4-2 answerThe scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the top 10% of students are given an A, what is the lowest mark a student can have and still be awarded an A?a. 63.28b. 70.97

c. 76.08 (correct)

62 + (1.28)(11)

1.4 Density Curves and Normal DistributionsSlide60

1.4-3The lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximatelya. 0.2000.b. 0.5793.

c. 0.4207.1.4 Density Curves and Normal DistributionsSlide61

1.4-3 answerThe lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximatelya. 0.2000.b. 0.5793.

c. 0.4207. (correct)

P

(

z >

0.20)

1.4 Density Curves and Normal DistributionsSlide62

1.4-4John and his father Bob both signed up for a 5K race but competed with different age groups. John finished his 5K in 19 minutes, while Bob finished his race in 20 minutes. The finish times of the 20–40 age group that John was a part of are Normally distributed with a mean of 18 minutes and a standard deviation of 0.7 minutes. The finish times of Bob’s 40–60 age group was Normally distributed with a mean of 19 minutes and a standard deviation of 2 minutes. How did the father and son fare with respect to their age groups? (Remember, in running, the lower the value, the faster they finished.)a. John did better.

b. Bob did better.c. They both did relatively the same.1.4 Density Curves and Normal DistributionsSlide63

1.4-4 answerJohn and his father Bob both signed up for a 5K race but competed with different age groups. John finished his 5K in 19 minutes, while Bob finished his race in 20 minutes. The finish times of the 20–40 age group that John was a part of are Normally distributed with a mean of 18 minutes and a standard deviation of 0.7 minutes. The finish times of Bob’s 40–60 age group was Normally distributed with a mean of 19 minutes and a standard deviation of 2 minutes. How did the father and son fare with respect to their age groups? (Remember, in running, the lower the value, the faster they finished.)a. John did better.

b. Bob did better. (correct)c. They both did relatively the same.

John’s

z

-score = (19 – 18)/0.7 = 1.4

Bob’s

z

-score = (20 – 19)/2 = 0.5

1.4 Density Curves and Normal DistributionsSlide64

1.4-5The most common intelligence quotient (IQ) scale is Normally distributed with mean 100 and standard deviation 15. Many school districts across the country seek to identify “gifted and talented” children for special enrichment programs. Typically, these children must have IQ scores in the top 5%. What is the minimum score to qualify a child for these programs?a. 130b. 125

c. 115

1.4 Density Curves and Normal DistributionsSlide65

1.4-5 answerThe most common intelligence quotient (IQ) scale is Normally distributed with mean 100 and standard deviation 15. Many school districts across the country seek to identify “gifted and talented” children for special enrichment programs. Typically, these children must have IQ scores in the top 5%. What is the minimum score to qualify a child for these programs?a. 130b. 125 (correct)

c. 115

(1.645)(15) + 100 = 124.675

1.4 Density Curves and Normal DistributionsSlide66

1.4-6Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. About what percent of young women in this age group will have cholesterol levels less than 150 mg/dl?a. 90%b. 18.5%

c. 81.5%1.4 Density Curves and Normal DistributionsSlide67

1.4-6 answerToo much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. About what percent of young women in this age group will have cholesterol levels less than 150 mg/dl?a. 90%b. 18.5% (correct)

c. 81.5%

1.4 Density Curves and Normal DistributionsSlide68

1.4-7Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. Cholesterol levels for middle-aged men vary Normally with mean 222 mg/dl and standard deviation 37 mg/dl. Sandy is a young woman with a cholesterol level of 220. Her father has a cholesterol level of 250. Who has relatively higher cholesterol?a. Sandy

b. Sandy’s fatherc. impossible to tell because of the scaling1.4 Density Curves and Normal DistributionsSlide69

1.4-7 answerToo much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. Cholesterol levels for middle-aged men vary Normally with mean 222 mg/dl and standard deviation 37 mg/dl. Sandy is a young woman with a cholesterol level of 220. Her father has a cholesterol level of 250. Who has relatively higher cholesterol?a. Sandy (correct)

b. Sandy’s fatherc. impossible to tell because of the scaling

Sandy’s

z

-score

1.4 Density Curves and Normal DistributionsSlide70

1.4-8What is the area under a density curve?a. 0b. 1

c. 21.4 Density Curves and Normal DistributionsSlide71

1.4-8 answerWhat is the area under a density curve?a. 0b. 1 (correct)

c. 21.4 Density Curves and Normal DistributionsSlide72

1.4-9The average of a standardized test is 1140 with a standard deviation of 150. About what percent of people will score at least a 1300?a. 86%b. 14%

c. 3%1.4 Density Curves and Normal DistributionsSlide73

1.4-9 answerThe average of a standardized test is 1140 with a standard deviation of 150. About what percent of people will score at least a 1300?a. 86%b. 14% (correct)

c. 3%

z

-score = (1300 – 1140)/150 = 1.4

1.4 Density Curves and Normal Distributions