Stats
Choose the data set whose mean is not equal to a value in the set.
4,4,7,7
What is the difference between a frequency polygon and an ogive?
A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.
How is a sample related to a population?
A sample is a subset of a population.
What is an inherent zero? Describe three examples of data sets that have inherent zeros and three that do not.
An inherent zero is a zero that implies none. Three examples of data sets that have inherent zeros below: Maximum wind speed during a hurricane Average monthly precipitation in inches Average age of college students in years Three examples of data sets that do not have inherent zeros below: Temperature in degrees Fahrenheit A student's level of happiness measured from 0 to 10 Average IQ score of a high school class
Outlier
An outlier is a data entry that is far removed from the other entries in the data set. Use the interquartile range to find the limit of the outliers. Any data entry less than [Q1-1.5(IQR)] or greater than [Q3+1.5(IQR)] is considered an outlier.
The years that your college football team won a championship are shown below. 1952 1974 1987 1988 1989 1993 2000 2010 2012 Determine the level of measurement of the data set. Explain your reasoning.
C. Interval. The data can be ordered and differences between data entries are meaningful, but a zero entry is not an inherent zero.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Data at the ordinal level are quantitative only.
False. Data at the ordinal level can be qualitative or quantitative.
What is a disadvantage of using a stem-and-leaf plot instead of a histogram?
Histograms easily organize data of all sizes where stem-and-leaf plots do not.
The graph to the right shows the number of that watch each sport in a local pub. Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. Horizontal reads "Sport" Vertical reads "# of people"
Horizontal = nominal Vertical = ratio
What is the difference between relative frequency and cumulative frequency?
Relative frequency of a class is the percentage of the data that falls in that class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
What is replication in an experiment? Why is replication important?
Replication is repetition of an experiment under the same or similar conditions. Replication is important because it enhances the validity of the results.
Determine whether the underlined number is a statistic or a parameter. A sample of professors is selected and it is found that 50% own a computer.
Statistic because the value is a numerical measurement describing a characteristic of a sample.
Use the Venn diagram to identify the population and the sample. A rectangular box reads, The income of home owners in a certain county, contains a smaller rectangular box that reads, The income of home owners in the county who have a garage.
The income of home owners in the county
How is a Pareto chart different from a standard vertical bar graph?
The bars are positioned in order of decreasing height with the tallest bar on the left.
Q1, first quartile
Use the median to divide the data set into two halves, excluding the median. Find the median of the lower half of the data set.
Q3
Use the median to divide the data set into two halves, excluding the median. Find the median of the upper half of the data set.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Tomatoes are planted on a 55-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.
What type of sampling is used? Stratified sampling is used, since the field is divided into subplots and a random sample is taken from each subplot. What potential sources of bias are present, if any? Select all that apply. Certain subplots may have more or fewer tomato plants than others. Samples from these subplots may bias the overall sample.
What is the difference between a random sample and a simple random sample?
With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
Relative frequency
class frequency/sample size
Chebychev's Theorem
states that the portion of any data set lying within k standard deviations (k>1) of the mean is at least 1-(1/k^2) This number can be expressed as a fraction or a percentage.
Determine whether the data set is a population or a sample. Explain your reasoning. The age of each member of the House of Representatives.
Population, because it is a collection of ages for all members of the House of Representatives.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
False. The method for selecting a systematic sample is to order a population in some way and then select members of the population at regular intervals.
The graph to the right shows the responses to question, "How serious is global warming?" Identify the level of measurement of the data listed on the horizontal and vertical axes in the graph. Horizontal reads "Response" Vertical reads "Percent"
Horizontal = ordinal Vertical = Ratio
Observational studies are sometimes referred to as natural experiments. Explain what this means.
In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.
What is the difference between an observational study and an experiment?
In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.
What are some benefits of using graphs of frequency distributions?
It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.
Why is a sample used more often that a population?
It is usually impossible to count the entire population.
The list of books that your friend read for school for the past five months is shown below. Kiss The Dead The Forgotten Spring Fever The Racketeer Gone Girl Identify the level of measurement of the data set. Explain your reasoning.
Nominal. The data are categorized using names, labels, or qualities, but the data cannot be ranked or arranged in order.
The jersey numbers for players on a basketball team are listed below. 6;10;47;17;20;15;9;5;19;12;24;18;8;30;4;7;14;1;42;27;22;25;34;23;68;29 Identify the level of measurement of the data set. Explain your reasoning.
Nominal. The data are categorized using numbers, but no mathematical computations can be made.
The following appear on a physician's intake form. Identify the level of measurement of the data. (a) Disabilities (b) Temperature (c) Time since last visit (d) Happiness level (scale of 0 to 10)
Ordinal
What are some benefits of representing data sets using frequency distributions?
Organizing the data into a frequency distribution can make patterns within the data more evident.
In a poll, 1,001 adults in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor. Identify the population and the sample.
Population = All adults in the country Sample = the 1,001 adults selected
Determine whether the data set is a population or a sample. Explain your reasoning. The number of garages for each house on a street.
Population, because it is a collection of the number of garages for all houses on the street.
A study of 894 senior citizens shows that participants who exercise regularly exhibit less of a decline in the cognitive ability than those who barely exercise at all. From this study, a researcher infers that your cognitive ability increases the more you exercise. What is wrong with this type of reasoning?
The inference may incorrectly imply that exercise increases a person's cognitive ability. The study shows a slower decline in cognitive ability.
Midpoint
The midpoint of a class is the sum of the lower and upper limits of the class divided by two.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Some quantitative data sets do not have medians.
The statement is false. All quantitative data set have medians.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect.
The statement is false. Double blinding is used to decrease the placebo effect.
Determine if the statement is true or false. If it is false, rewrite it as a true statement. It is impossible for the Census Bureau to obtain all the census data about the population of the United States.
The statement is true.
determine whether the following statement is true or false. If it is false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.
The statement is true.
A student's IQ score is in the 91st percentile on an intelligence scale. Make an observation about the student's IQ score.
The student has a higher IQ score than 91% of the students in the same age group.
A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score?
The student scored higher than 78% of the students who took the actuarial exam.
Determine whether the study is an observational study or an experiment. Explain. In a survey of 13511 adults in a country, 54% said the country's leader should release all medical information that might affect their ability to serve.
The study is observational, because it does not apply a treatment to the adults.
What is the definition of mean?
The sum of the data entries divided by the number of entries.
What are the two main branches of statistics?
The two main branches of statistics are descriptive statistics and inferential statistics.
Why is the standard deviation used more frequently than the variance?
The units of variance are squared. Its units are meaningless.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Case ID numbers at a law firm
The variable is qualitative because numbers of spots are attributes or labels.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Goals scored in a hockey game
The variable is quantitative because goals scored is found by measuring or counting
A data set includes the entries 2,5,7,9,9, and 12. Complete the data set with an entry between 1 and 12 so that the median and mode of the set are equal.
9
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum equals=13, maximum equals=96, 7 classes
The class width is 12. Use the minimum as the first lower class limit, and then find the remaining lower class limits. The lower class limits are 13, 25, 37, 49, 61, 73, 85. The upper class limits are 24,36,48,60,72,84,96.
What is the definition of mode?
The data entry that occurs with the greatest frequency.
Population variation
The deviation of an entry, x, in a data set is the difference between the entry and the population mean. The population variance is the sum of the squares of these deviations divided by the number of entries.
Sample variance
The deviation of an entry, x, in a data set is the difference between the entry and the sample mean. The sample variance is the sum of the squares of these deviations divided by the number of entries minus one (n−1).
Suppose a survey of 580 women in the United States found that more than 70% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.
There is an association between U.S. women and being the primary investor in their household.
Determine whether the data set is a population or a sample. Explain your reasoning. The salary of 16 teachers in a school.
This is a sample, because it is a collection of salaries for some teachers in the school.
A company has been rating television programs for more than 60 years. It uses several sampling procedures, but its main one is to track the viewing patterns of 20,000 households. These contain more than 45,000 people and are chosen to form a cross section of the overall population. The households represent various locations, ethnic groups, and income brackets. The data gathered from the sample of 20,000 households are used to draw inferences about the population of all households in the United States. Complete parts (a) and (b) below.
What strata are used in the sample? Choose the correct answer below. The various locations, ethnic groups, and income brackets that are represented Why is it important to have a stratified sample for these ratings? Choose the correct answer below. Stratified sampling ensures that each segment of the population is represented.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. Assume the population of interest is the student body at a university. Questioning students as they leave a university library, a researcher asks 363 students about their eating habits.
What type of sampling is used? Convenience sampling is used, because students are chosen due to convenience of location. What potential sources of bias are present, if any? Select all that apply. Because of the personal nature of the question, students may not answer honestly. The sample only consists of members of the population that are easy to get. These members may not be representative of the population.
Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same.
1,1,6,6,6,8,8
Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you eat fast food during an average month? Is the question biased?
No, because it does not lead the respondent to any particular answer.
Determine whether the data set is a population or a sample. Explain your reasoning. The heights of half of the students in a class
Sample, because the collection of heights of half of the students is a subset of all students in the class.
What is an advantage of using a stem-and-leaf plot instead of a histogram?
Stem-and-leaf plots contain original data values where histograms do not.
Use the row of numbers shown below to generate 12 random numbers between 01 and 99. 97089 45460 72343 26103 11275 10784 29958 09902 Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
1: 97 2: 8 3: 94 4: 54 5: 60 6: 72 7: 34 8: 32 9: 61 10: 3 11: 11 12: 27
What is the difference between a census and a sampling?
A census includes the entire population. A sampling includes only part of the population.
What is the difference between class limits and class boundaries?
Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits and class boundaries differ by 0.5.
Suppose a survey of 915 homeowners found that more than 29% bought flood insurance. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey.
Descriptive = 29% of homeowners in the sample bought flood insurance. Inferential = Most homeowners do not buy flood insurance.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. More types of calculations can be performed with data at the nominal level than with data at the interval level.
False. More types of calculations can be performed with data at the interval level than with data at the nominal level.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Using a systematic sample guarantees that members of each group within a population will be sampled.
False. Using a stratified sample guarantees that members of each group within a population will be sampled.
Q2, second quartile
Find the median or second quartile. About one half the data fall on or below the second quartile (the second quartile is the same as the median of the data set).
Select all the levels of measurement for which data can be quantitative.
Interval Ordinal Ratio
What is an advantage of using the range as a measure of variation?
It is easy to compute.
What is a disadvantage of using the range as a measure of variation?
It uses only two entries from the data set.
Select all the levels of measurement for which data can be qualitative.
Nominal Ordinal
Determine whether the underlined value is a parameter or a statistic. The average age of men who have walked on the moon was 39 years, 11 months, 15 days.
Parameter
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Weights of pumpkins at a fair
The variable is quantitative because weights are numerical measurements.
A survey of 12,080 women in a particular country found that 46.9% received an influenza vaccine for a recent flu season. Identify the population and the sample.
Population = The immunization status of all women in the country Sample = The immunization status of the 12,080 women selected
A polling organization contacts 1754 adult women who are 30 to 70 years of age and live in the United States and asks whether or not they had received a mammogram during the past year.
Population = adult women who are 30 to 70 years of age and live in the United States Sample = the 1754 adult women who are 30 to 70 years of age and live in the United States
The heights (in centimeters) of a sample of a species of plant 30 days after sprouting are shown below. 22.6 19.3 20.3 22.3 17.2 21.6 21.8 18.8 20.7 Determine whether the data are qualitative or quantitative and identify the data set's level of measurement.
Quantitative Ratio
What technology format could be used to generate eleven random numbers between 1 and 750?
RandInt(1,750750,1111)
Interquartile Range
The interquartile range (IQR) of a data set is a measure of variation that gives the range of the middle portion (about half) of the data. The IQR is the difference between the third and first quartiles and is given by the following formula: IQR= Q3-Q1
Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. 65 of the 92 passengers aboard an airship survived an explosion
The number is a population parameter because it is a numerical description of all of the passengers that survived.
Determine whether the underlined number describes a population parameter or a sample statistic. Explain your reasoning. A survey of 2216 adults in a country found that 82% think that militant terrorists are a major threat to the well-being of their country.
The number is a sample statistic because it describes the people in a sample, which is a subset of all of the people in the country.
Determine if the survey question is biased. If the question is biased, suggest a better wording. Why is walking every day good for you?
The question is biased. The wording "How do you think walking every day affects your health?" would be better.
Explain how to find the range of a data set. Choose the correct answer below.
The range is found by subtracting the minimum data entry from the maximum data entry.
How does changing the maximum value affect the range?
The range is greatly affected by this change.
Population standard deviation
The standard deviation is equal to the square root of the variance, rounding to the nearest tenth.
Sample standard deviation
The standard deviation is equal to the square root of the variance, rounding to the nearest tenth.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A placebo is an actual treatment.
The statement is false. A placebo is a fake treatment.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. Data at the ratio level cannot be put in order.
The statement is false. A true statement is "Data at the ratio level can be placed in a meaningful order."
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. For data at the interval level, you cannot calculate meaningful differences between data entries.
The statement is false. A true statement is "For data at the interval level, you can calculate meaningful differences between data entries."
Determine whether the study is an observational study or an experiment. Explain. To study the effects of social media on teenagers' brains, researchers showed a few dozen teenagers photographs that had varying numbers of "likes" while scanning the reactions in their brains.
The study is an experiment, because it applies a treatment to the teenagers.
What is the definition of median?
The value that lies in the middle of the data when the data set is ordered.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Model numbers
The variable is qualitative because model numbers are attributes or labels.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite basketball player
The variable is qualitative because a favorite player describes an attribute or characteristic.
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Amount of disk space in gigabytes
The variable is quantitative because amount of disk space is found by measuring or counting.
Identify the sampling techniques used, and discuss potential sources of bias (if any). Explain. After a tsunami, a disaster area is divided into 150 equal grids. Forty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most.
What type of sampling is used? Cluster sampling is used, since the disaster area is divided into grids, and some of those grids are selected and everyone in those grids is interviewed. What potential sources of bias are present, if any? Select all that apply. Certain grids may have been much more severely damaged than others. The grids that are selected may not be representative in terms of damage. Certain grids may have been much more severely damaged than others. Severely damaged grids may have fewer occupied households.
