Deck 5: Exploring Data: Distributions

Question 1

Two towns both have a mean income for their residents of $30,000. The standard deviation of incomes of residents in town A is $2600, and the standard deviation of incomes of residents in town B is $25,000. Explain what this says about the difference in the distribution of incomes in the two towns.

Answer 1

In town A, the mean income is $30,000 and almost all residents earn between $20,000 and $40,000. The standard deviation of $2600 says incomes do not vary much among residents of the town. In town B, since the standard deviation is $25,000, we know that there are very poor residents and very rich residents even though the mean income is also $30,000.

Question 2

Below is a histogram of car prices on a used-car lot. An advertisement for the lot says the average price of a car for sale is $12,000. Could the advertisement be true? Why or why not?

Answer 2

Yes, the advertisement could be True. The presence of a car or cars with a sale price of $200 (the outlier(s) on the histogram) could lower the mean sale price to $12,000.

Question 3

Below is a histogram for a set of data. Would you use the five-number summary or the mean and standard deviation to describe these data? Why?

Answer 3

Since the distribution is skewed, the five-number summary would be the better choice to describe the data shown in the histogram.

Question 4

After computing the standard deviation for a set of measurements, you notice your answer is negative. Is this possible?

Question 5

Suppose you discover that the outlier 120.0 was recorded incorrectly: It really should be 20.0. When you change 120.0 to 20.0, is the new median larger, smaller, or the same?

Question 6

The data below represent the numbers of auto accidents at a certain intersection each month for a year. Find the range of the data. 0, 1, 3, 4, 5, 2, 2, 6, 7, 2, 0, 1

Question 7

In the list of five measurements shown below, one is blurred. What MUST this value be, if the mean of the five measurements is 7?

Question 8

What is the difference Q₃ − Q₁ for this data set?

Question 9

What is the median of this data set?

Question 10

Below are the ages of students attending an art exhibit. Find the mean age of the students.
11, 11, 12, 12, 13, 1 3, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18

Question 11

In a normal distribution with mean 100 and standard deviation 7, which value is more common: a value between 100 and 107, or a value outside the range 93 to 107?

Question 12

Below are the ages of six patients seen by a pediatrician on one day. Find the standard deviation of the ages. 3, 7, 9, 9, 15, 18

Question 13

Below are the ages of six patients seen by a pediatrician on one day. Find the standard deviation of the ages. 3, 6, 7, 9, 15, 20

Question 14

A data set consists of measurements of lengths in centimeters. What is the unit of the standard deviation?

Question 15

Could it be possible that the standard deviation is 0?

Question 16

What is the range of this data set?

Question 17

Find the standard deviation of the following set of measurements. 4, 7, 9, 11, 13, 22

Question 18

Find the mean of the following set of data:
23, 45, 26, 18, 11, 42, 35, 16, 32

Question 19

Find the standard deviation of the following set of data: 5, 7, 17, 31, 45, 47, 68, 85, 96, 99

Question 20

A student earned three midterm scores as 80, 75, 70 and a final test is left. What is the lowest final score if she wants to get the mean of test scores at least 80?

Question 21

Create a set of five positive numbers that have median 8 and mean 6.

Question 22

Based on the histogram, which statement must be true?

A) There are no gaps in the histogram.
B) Eight patients waited exactly 35 minutes.
C) Two patients were seen immediately on arrival at the clinic.
D) More patients waited longer than one half-hour than waited less than one half-hour.

Question 23

Based on the histogram, which statement is true?

A) The histogram is roughly symmetric.
B) The class from 50 to 59 minutes represents 10 outliers.
C) There is a gap in the histogram.
D) The histogram is skewed to the right.

Question 24

Below are listed the ages (in months) of children at a daycare center. Choose the correct stemplot of the data.
18, 24, 25, 35, 37, 42, 47, 48, 48, 58

A)
$\begin{array}{l|l}1 & 8 \\2 & 45 \\3 & 57 \\4 & 278 \\5 & 8\end{array}$
B)
$\begin{array}{l|l}1 & 8 \\2 & 45 \\3 & 57 \\4 & 2788 \\5 & 8\end{array}$
C)
$\begin{array}{l|l}1 & 1 \\2 & 2 \\3 & 2 \\4 & 4 \\5 & 1\end{array}$
D)
$\begin{array}{l|l}1 & 18 \\2 & 24,25 \\3 & 35,37 \\4 & 42,47,48 \\5 & 58\end{array}$

Question 25

In the list of five measurements shown below, one is blurred. Supply a fifth value that would make the median 5.

Question 26

The scores of students on a standardized test form a normal distribution with a mean of 300 and a standard deviation of 40. Two thousand students took the test. Find the number of students who score above 380.

Question 27

Below are listed the numbers of children in the classrooms of a small elementary school. Choose the correct stemplot of the data.
12, 14, 20, 21, 21, 25, 27, 30, 30, 30

A)
$\begin{array}{l|l}1 & 12,14 \\2 & 20,21,27 \\3 & 30\end{array}$
B)
$\begin{array}{l|l}1 & 2 \\2 & 5 \\3 & 3\end{array}$
C)
$\begin{array}{l|l}1 & 24 \\2 & 01157 \\3 & 000\end{array}$
D)
$\begin{array}{l|l}1 & 24 \\2 & 0157 \\3 & 0\end{array}$

Question 28

The average length of time, per week, that students at a certain university spend on homework is normally distributed with a mean of 24.3 hours and a standard deviation of 1.4 hours. Jane tells her parents she spends more time studying than 75% of the students on campus. How many hours per week must Jane spend on homework for this to be true?

Question 29

Use the data set
3, 4, 5, 6, 7.
What value could you add to this data set that will cause the median to decrease while the range remains same?

Question 30

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon:
53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123
Make a boxplot to represent these data.

Question 31

Use the data set
7, 8, 9, 10.
What value can you add to this data set that will make the median equal to 8.5?

Question 32

Create a set of five positive numbers that have median 6 and mean 10.

Question 33

In the list of five measurements shown below, one is blurred. Supply a fifth value that would make the median 8.

Question 34

The distribution of the scores on a standardized exam is approximately normal with mean 400 and standard deviation 35. Between what two values do the middle 50% of scores lie?

Question 35

Use the following histogram of waiting times for patients at a health clinic to answer Questions 6-8.
How many patients waited between 20 and 29 minutes?

A) 2
B) 3
C) 6
D) 8

Question 36

Would you expect the mean salary of WNBA basketball players to be larger than the median salary or smaller than the median salary?

Question 37

Given the stemplot below, which description is true?

A) The number 1 is the only outlier on the stemplot.
B) The distribution is right-skewed.
C) The median is 21.
D) The range is 33.

Question 38

The scores of students on a standardized test form a normal distribution with a mean score of 500 and a standard deviation of 100. Between what two values do the middle 50% of scores lie?

Question 39

Given the stemplot below, which description is true?

A) There are no outliers on the stemplot.
B) The numbers 29 and 75 are outliers on the stemplot.
C) The number 75 is the only outlier on the stemplot.
D) The number 60 is the only outlier on the stemplot.

Question 40

Given the stemplot below, which description is true?

A) There are no outliers on the stemplot.
B) The number 29 is the only outlier on the stemplot.
C) The numbers 29 and 75 are the only outliers on the stemplot.
D) The number 75 is the only outlier on the stemplot.

Question 41

Use the following information to answer Questions 24-27.
Below are the numbers of errors made by a typist on various pages of typing.
14, 6, 12, 19, 2, 35, 5, 4, 3, 7, 5, 8
Find the mean number of errors.

A) 6.5
B) 7
C) 9.583
D) 10

Question 42

What is the standard deviation of the ages?

A) 26.4
B) 20.6
C) 19.9
D) 4.5

Question 43

Below is a histogram of the ages of people attending a concert. Which statement is true?

A) The histogram is roughly symmetric.
B) There is a gap in the histogram.
C) The histogram is skewed to the left.
D) The center of the distribution is at about age 50.

Question 44

Use the following information to answer Questions 18-23.
Below is a list of the number of dogs owned by families in a particular neighborhood.
0, 0, 2, 1, 0, 1, 0, 4, 0, 1
What is the mean number of dogs owned?

A) 0
B) 0.5
C) 0.9
D) 1.29

Question 45

Find the median number of errors.

A) 6.5
B) 7
C) 9.583
D) 10

Question 46

Given the set of data below, find the mean.

A) 4.5
B) 5
C) 7
D) 30

Question 47

Find the third quartile for the number of errors.

A) 5
B) 13
C) 15.5
D) 4.5

Question 48

Given the histogram below, which statement is true?

A) The histogram has an outlier between 400 and 500.
B) The histogram is skewed to the right.
C) The histogram is symmetric.
D) The histogram has a gap between 400 and 500.

Question 49

Below are the heights (in inches) of students in a third-grade class. Find the median height.

A) 47.5
B) 50
C) 46.0625
D) 47

Question 50

Use the following information to answer Questions 12-15.
Below are the ages of 15 students in a college class.
27, 50, 33, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28
What is the median age?

A) 34
B) 31
C) 41.3
D) 20.6

Question 51

What is the third quartile for these data?

A) 0
B) 0.5
C) 1
D) 1.5

Question 52

Find the first quartile for the number of errors.

A) 5
B) 13
C) 15.5
D) 4.5

Question 53

What is the standard deviation for these data?

A) 0.91
B) 1.11
C) 1.22
D) 1.29

Question 54

What is the first quartile for these data?

A) 0
B) 0.5
C) 1
D) 1.5

Question 55

Below are the heights (in inches) of students in a third-grade class. Find the mean height.

A) 47.5
B) 50
C) 46.0625
D) 47

Question 56

What is the mean age?

A) 34
B) 31
C) 41.3
D) 20.6

Question 57

What is the range of the middle 50% of the ages, Q₃ - Q₁?

A) 23
B) 34
C) 50
D) 66

Question 58

What is the range for these data?

A) 1
B) 2
C) 3
D) 4

Question 59

Given the histogram below, which statement is true?

A) The histogram has a gap.
B) There is an outlier at 100.
C) The histogram is skewed to the left.
D) The histogram is roughly symmetric.

Question 60

What is the median number of dogs owned?

A) 0
B) 0.5
C) 0.9
D) 1.29

Question 61

Below are the lengths (in minutes) of phone calls made to a business on one day. Find the five-number summary for these data.

A) 5, 8, 14, 15.5, 20
B) 2, 4, 7, 14, 35
C) 2, 4, 6, 12, 19
D) 2, 4.5, 6.5, 13, 35

Question 62

For Questions 48-52, use the following data sets:
Set A: 1, 2, 3, 4
Set B: 1, 1, 4, 7
Set C: 0, 5, 5, 10
Set D: 6, 6, 6, 6
Which data set has standard deviation 0?

A) Set A
B) Set B
C) Set C
D) Set D

Question 63

Given the set of data below, find the standard deviation.

A) 2.37
B) 4.5
C) 4.74
D) 5.6

Question 64

Given the set of data below, find the mean.

A) 34.5
B) 31
C) 31.5
D) 50

Question 65

Given the set of data below, find the median.

A) 4.5
B) 5
C) 7
D) 30

Question 66

Given the set of data below, find the range.

A) 2
B) 4
C) 7
D) 9

Question 67

Given the set of data below, find the standard deviation.

A) 6.07
B) 13.58
C) 184.3
D) 921.5

Question 68

Given the set of data below, find the median.

A) 34.5
B) 31
C) 31.5
D) 50

Question 69

Questions refer to the following frequency distribution:
If the data set contains 20 values, how many of them are 3?

A) 6
B) 4
C) 3
D) 2

Question 70

Use the following information to answer Questions 36-39.
Below are the numbers of pages in each of seven chapters of a textbook.
14, 14, 20, 38, 47, 48, 57
What is the mean number of pages?

A) 34
B) 38
C) 37.33
D) 42.5

Question 71

Consider the following data set: 1, 1, 3, 3, 6, 6, 6, 9, 11, 11
What is the relative frequency of the value 6?

A) 6/11
B) 2/11
C) 4/10
D) 3/10

Question 72

Questions refer to the following frequency distribution:
If the data set contains 20 values, what is the median?

A) 2
B) 2.5
C) 3
D) 3.5

Question 73

What is the standard deviation?

A) 18.52
B) 18
C) 17.82
D) 17.67

Question 74

Below are the scores of 21 students on a history exam. Find the five-number summary of the scores.

A) 50, 65, 75, 85, 100
B) 50, 65, 75, 87.5, 100
C) 50, 65, 76.9, 87.5, 100
D) 50, 65, 77.5, 90, 100

Question 75

Questions refer to the following frequency distribution:
Which of the following statements describes the mean of the distribution?

A) It is less than 2.
B) It is between 2 and 3.
C) It is larger than 3.
D) The mean cannot be determined from the frequency distribution.

Question 76

Which of the following statements about measures of the center of a distribution of data is true?

A)
Neither the mean nor the median is strongly affected by an outlier in the data.
B)
The mean is strongly affected by an outlier in the data, but the median is not.
C)
The median is strongly affected by an outlier in the data, but the mean is not.
D)
Both the mean and the median are strongly affected by an outlier in the data.

Question 77

What is the median number of pages?

A) 34
B) 38
C) 37.33
D) 42.5

Question 78

Given the set of data below, find the range.

A) 12
B) 34
C) 50
D) 66

Question 79

What is the range?

A) 14
B) 38
C) 43
D) 71

Question 80

Below are the numbers of accidents occurring at a certain corner on 15 consecutive days. Find the five-number summary of the data.

A) 0, 1.5, 3.5, 5.5, 7
B) 0, 1, 3, 5, 7
C) 0, 4, 6, 1, 3
D) 0, 1.5, 3, 5.5, 7