DE Statistics Exam 1

A time series graph represents data that occur a specific time period. True or false

True

A weighted mean is used when the values of the data set are not equally represented. True of false

True

An ogive is also called a cumulative frequency graph. True or false

True

Graphs give a visual representation that may enable readers to analyze and interpret data more easily than simply looking at tables of numbers. True or false

True

The cumulative frequency for a class is the sum of the frequencies of the classes less than and equal to the upper boundary of the specific class. True or false

True

The frequency polygon and the histogram are two different ways to represent the same data set. True or false

True

The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. True or false

True

The median can be a more appropriate measure of central tendency if the distribution of the data is extremely skewed. True or false

True

The percentile corresponding to a given data value X is computed by adding the 0.5 to number of values less than X then dividing by the total number of values in the data set. True or false

True

The ___ is the average of the squares of the distance each value is from the mean.

Variance

The ___ and _____ are two measures of variation used to describe the spread of the data in a data set.

Variance and standard deviation

How many ways can a student select five questions from an exam containing 10 questions, if one of the last five must be the last question?

126

What is the lower class limit of 13-17?

13

According to Chebyshev's theorem the maximum proportion of data values from a data set that are more than 2 standard deviations from the mean is

.25

A population has a mean of 15 and a standard deviation of 14. Find the z-score for a population value of 20.

.4

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 289 mm with a standard deviation of 40 mm. For pompano, the mean is 158 mm with a standard deviation of 36 mm. Stewart caught a bluefish that was 311 mm long. What was the z-score for this length?

.6

The average weight of adult male bison in a particular federal wildlife preserve in 1750 pounds with a standard deviation of 270 pounds. Find the weight of an adult bull whose z-score is -2.5.

1,075 pounds

A baseball player has a batting average of 0.325 each week of the season, with a standard deviation of 0.065. What is the z score when he bats 0.410 one week?

1.3

If a student scored 87 points on a test where the mean score was 81.2 and the standard deviation was 3.7. The student's z-score is

1.6

For the data set below, find the IQR. 71, 69, 62, 79, 64, 79, 63, 66, 72, 74, 65

10

The costs per load (in cents) of 28 dish-washing detergents tested by a consumer organization are shown here. Find the standard deviation of the sample. Class limits Frequency 20-28 8 29-37 11 38-46 2 47-55 7

10.35

The average age of Stokes County school board members over the last 40 years has been 56, but members have ranged from 29 to 72. Use the range rule of thumb to estimate the standard deviation of the members' ages.

10.8

What is the midrange of the following data set? 5,11,10,12,4,12,18,18,18

11

Evaluate the permutation: 4 P 2

12

Use the given frequency distribution to approximate the mean Class Frequency 0-4 11 5-9 15 10-14 16 15-19 16 20-24 11

12.1

If a set of data has a mean 48 and variance 36, then it's coefficient of variation is

12.5%

A store manager wants to display 5 different brands of toothpaste in a row. How many ways can this be done?

120

A consumer advocacy group tested the "on-air" lifetimes a random sample of 191 cell phone batteries. The mean lifetime was 2.8 hours with a standard deviation of 0.5 hours. The lifetimes are approximately bell-shaped. Estimate the number of batteries with lifetimes between 2.3 and 3.3 hours.

130

On a tv game show, a contestant is shown 11 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen items need not be in any particular order. In how many ways can the contestant choose the three items?

165

There are 3 different math courses, 3 different science courses, and 2 different history courses. If a student must take one of each, how many different ways can this be done?

18

Determine the range for the following data set. 4,7,3,16,5,22,8

19

A student received the following grades last semester. Find the student's semester grade point average. Course Credits Grade/points Statistics 4 A/4.0 Physics 5 C/2.0 Sociology 3 B/3.0 Literature 2 B/3.0 Tennis 1 D/ 1.0

2.80

A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?

210

For the data below, find the upper outline boundary. 160, 176, 193, 144, 163, 146, 152, 158, 154, 184, 129

221

A furniture manufacturer offers bookcases in 6 different sizes and 4 different colors. If every color is available in every size, then the total number of different bookcases is

24

The average weekly earnings in dollars for various industries are listed below. Find the percentile rank of 717. 841, 717, 653, 775, 686, 796, 873, 600, 911, 954

35th percentile

Evaluate the factorial: 9!

362,880

How many different ways can a teacher select 3 students from a class of 17 students to each perform a different classroom task?

4,080

Evaluate the combination: 11 C 6

462

Find the population variance for the following data set: 23,11,30,13,16

49.0

Find the mode for the following data (5,4,3,4,5,6,5,5,3,4)

5

Given the following data set, find the approximate value that corresponds to the 75th percentile. 10, 44, 15, 23, 14, 18, 72, 56

50

The average resident of Metro City produces 700 pounds of solid waste each year, and the standard deviation is approximately 90 pounds. Use Chebyshev's theorem to find the weight range that contains at least 75% of all residents' annual garbage weights

520-880 pounds

If a data set has 25 values and a standard deviation 7.4, then the variance is

54.8

Find the sample standard deviation for the following data set: 29,18,15,23,14

6.2

Check the following data set for outliers. 63, 72, 74, 74, 76, 77, 79, 81

63

A paint manufacturer discovers that the mean volume of paint in a gallon-sized pail is 1.1 gallons with a standard 0.1 gallons. The paint volumes are approximately bell-shaped. Estimate the percent of pails with volumes between 1.00 and 1.20 gallons.

68%

If a frequency distribution had class limits of 132-138, what would be the class width?

7

a soft-drink bottling company fills and ships soda in plastic bottles with a target volume of 354 mm. The filling machinery does not deliver a perfectly consistent volume of liquid to each bottle, and the three quartiles for the fill volume are Q1=352, Q2= 357, and Q3= 359. Find the IQR.

7

If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

720

A Pareto chart does not have which of the following properties? A) quantitative variable on the horizontal axis B) frequencies arranged from highest to lowest C) frequencies displayed by the heights of vertical bars D) classes of data are categorical

A

A club has 10 members. There are 720 ways that a chairperson, a secretary, and a treasurer can be selected from these 10 members. Assume a person can hold, at most, one office. A) True B) False

A

A soft-drink bottling company fills and ships soda in plastic bottles with a target volume of 354 mm. The filling machinery does not deliver a perfectly consistent volume of liquid to each bottle, and the three quartiles fill volume are Q1=353, Q2=356, and Q3=359. A fill volume of 346 mL is considered low. Would a fill volume of 346 mL be considered an outlier? A) No B) Yes

A

One hundred students are shown an eight- digit number on a piece of cardboard for three seconds and are asked to then recite the number from memory. The process is repeated until the student accurately recites the entire number from memory. The following histogram presents the number of trials it took each student to memorize the number. How many students memorized the number in three trials or less? A) 87 B)16 C) 3 D) 13

D

Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 287 mm with a standard deviation of 61 mm. For pompano, the mean is 147 mm with a standard deviation of 30 mm. Stewart caught a bluefish that was 306 mm long, and Gina caught a pompano that was 187 mm long. Who caught the longer fish, relative to fish of the same species? A) Gina B) Neither. Relative to its respective species, the fish are the same length C) Stewart

A

Greg wants to construct a frequency distribution for the political affiliation of the employees at Owen's Hardware Store. What type of distribution would be best? A) categorical B) ungrouped C) grouped D) cumulative

A

There are 2,368 possible ways that a committee of eight people can be selected from a group of 14 people. A) False B) True

A

A time series graph is useful for which of the following purposes? A) representing the frequencies of the data, sorted from largest to smallest B) representing the changing frequencies of a data category over a period of time C) representing the cumulative frequencies of the data at a specific time D) representing relative frequencies of categories at a specific time

B

In an ungrouped frequency distribution of the average age of high school graduates, what would be the boundaries for the class of graduates who were reported to be 18 years old? A) 17.6-19.5 years old B) 17.5-18.5 years old C) 17-19 years old D) 17.6-18.5 years old

B

Using the ogive below, what is the cumulative frequency of data values less than or equal to 16? A)60 B)30 C)20 D)66

B

What is the midpoint of the class 9-13? A) 11.5 B) 11 C) 5 D) 4

B

When making Pareto charts, data should be arranged ___ according to frequency A) clockwise B) from largest to smallest C) from smallest to largest D) with increasing time

B

Which of the following could be an ogive? A) a gradually descending curve that does not touch the x-axis B) a gradually ascending curve that starts at the x-axis C) a graph that has many peaks that ends in a negative direction D) a graph that has a few peaks and ends in a positive direction

B

Which of the following does not need to be done when constructing a frequency distribution? A) use classes that are mutually exclusive B) make the class width an even number C) select the number of classes desired D) find the range

B

A characteristic or measure obtained by using all the data values for a specific population is called a ____ A) variable B) mode C) parameter D) statistic

C

A pie graph is not useful in showing which of the following characteristics of a data set? A) relative frequencies for each category in the distribution B) categories that make up the largest proportions of the total C) frequency changes over time D) categories that make up the smallest proportions of the total

C

A weatherman records the amount of rain that fell in Portland, Oregon each day for a year. What type of graph should he use to show how rainfall changes during the year? A) Pareto chart B) Pictograph C) Time series graph D) Pie graph

C

Classify the histogram as skewed to the left, skewed to the right, or approximately symmetric. (since a picture can't be provided, note that the graph getting smaller) A) approximately symmetric B) skewed to the left C) skewed to the right

C

For the class 5-23, the upper class limits is A) 4.5 B) 5 C) 23 D) 23.5

C

Graphs that show distributions using proportions instead of raw data as frequencies are called A) Histograms B) Frequency Polygons C) Relative frequency graphs D) Ogive graphs

C

In a unimodal, symmetrical distribution as shown in the figure below A) the median and the mode are the same, but the mean can be different B) the mean is the same as the median, but the mode can be different C) the mean, the median, and the mode are the same D) the mean, the median, and the mode are different

C

Indicate which student has the higher z score. Art major: X=46 X bar= 50.5 s=5.2 Theater major: X=70 X bar= 75.1 s=7.3 A) The art major has a higher score than the theater major B) Neither student received a positive score; therefore, the higher score cannot be determined C) The theater major has a higher score than the art major D) Both students have the same score

C

The following frequency distribution presents the frequency of passenger vehicles that pass through a certain intersection from 8:00 AM to 9:00 AM on a particular day. vehicle type: motorcycle Frequency: 6 Sedan Frequency: 69 SUV Frequency: 86 Truck Frequency: 46 what is the relative frequency of the SUV category? A) 1 B) 86% C) 0.415 D) 86

C

Thirty students recorded the colors of their eyes, choosing from the colors brown, blue, green, hazel, and black. This data can be appropriately summarized in a A) upper boundary B) open-ended distribution C)categorical frequency distribution D)grouped frequency distribution

C

Which graph should be used to represent the frequencies with which certain courses are taken at Highlands Middle School? A) time series graph B) pie graph C) Pareto chart D) pictograph

C

Which of the following is the properly rounded mean for the given data? 7,8,13,9,10,11 A) 9 B) 9.67 C) 9.7 D) 10

C

A distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to A) a boxplot B) a symmetrical distribution C) differential statistics D) the empirical rule

D

The following time-series plot presents the population growth (in percent) of a suburb of Atlanta, Georgia for each of the years 1990 through 2009. Estimate the amount by which the rate of growth changed from 2004 to 2007. A) about 3.4 percentage points B) about 2.1 percentage points C) about 1.8 percentage points D) amount 2.7 percentage points

D

The following time-series plot presents the population growth (in percent) of a suburb of Atlanta, Georgia for each of the years 1990 through 2009. Estimate the rate of growth in 2009. A) 3.6% B) 3.3% C) 3.5% D) 4.2%

D

What are the boundaries of the class 12-15? A) 12 and 15 B) 3 C) 10.5 and 16.5 D) 11.5 and 15.5

D

What is the median of the following set of values? 1,15,13,9,13,8,9,13 A) 13 B) 9 C) 7 D) 11

D

Which of the following is true? A) D5=P5=Q5 B)D50=P5=Q25 C)D50=P5=Q2 D)D5=P50=Q2

D

Which of the following pairs of class limits would be appropriate for grouping the numbers 5,8,3, and 10? A) 3-5 and 6-10 B) 2-6 and 6-10 C) 3-5 and 8-10 D) 3-6 and 7-10

D

Give the degrees and percentage of each cookie type for a pie graph Cookie types: chocolate chip # sold: 20 Peanut butter #sold: 15 Oatmeal # sold: 30 Sugar # sold: 10

Degrees: 96 72 144 48 Percent: 27% 20% 40% 13% Total: 75 and 100%

A Pareto chart is useful for showing percentages of the total at different times. True or false

False

A pie graph would best represent the number of inches of rain that has fallen in Ohio each day for the past two months. True or false

False

For a given data set, the ogive and the frequency polygon will have the same overall shape True or False

False

The interquartile range IQR is found by subtracting the mean from the maximum value of a data set. True or false

False

The __ of a specific class is the number of data values contained in it

Frequency

The three most commonly used graphs in research are the histogram, the ____, and the cumulative frequency graph (ogive).

Frequency polygon

When the range is large and classes that are several units in width are needed, a __________ frequency distribution is used.

Grouped

A ___ is the midpoint in a data array

Median

The _____ is the mode for grouped data

Modal class

___ are either extremely high or extremely low data values compared with the rest of the data.

Outliers

The percentages of white, wheat, and rye bread sold at a supermarket each week is best shown using a ___ graph.

Pie

____ divide a distribution into four groups, and ____ divide a distribution into ten groups.

Quartiles and deciles

When data are collected in original form, they are called __________.

Raw data

If the graph of a frequency distribution has a peak and the data tapers off more slowly to the right and more quickly to the left the distribution is said to be ____________________

Right skewed

A ___ graph would most appropriately represent the number of students that were enrolled in statistics for each of the past ten years.

Time series

A time series graph is useful for detecting trends that occur over the period of time. True or false

True