Intro to Statistics Reading Quiz Chpt 1-3

The numbers used to separate the classes of a frequency​ distribution, but without the gaps created by class​ limits, are called

class boundaries.

A ____ is found by adding the lower and upper class limit and then dividing the sum by 2.

class midpoint

The _______ is the difference between two consecutive lower class limits or two consecutive upper class limits.

class width

A​ __________ sample is obtained by dividing the population in groups and selecting all the individuals in randomly selected groups.

cluster

A quantitative variable has an infinite number of possible values that are not countable is called _______

continuous

A ____ sample is obtained by selecting individuals who are easily contacted or those who voluntarily respond.

convenience

In a​ _______ study, data are​ observed, measured, and collected at one point in time.

cross-sectional

The​ ____________________ for a class is the sum of the frequencies for that class and all previous classes.

cumulative class frequency

After constructing any relative frequency​ distribution, what should be the sum of the relative​ frequencies? Choose the correct answer below. a. the sample size b. the total of all class frequencies c. 0 d. 1 or​ 100%

d. 1 or​ 100%

In a typical​ boxplot, the length of the box indicates which measure of​ spread? Choose the correct answer below. a. Range b. Standard deviation c. Variance d. Interquartile range​ (IQR)

d. Interquartile range​ (IQR)

A quantitative variable that has a finite or countable number of values is called​ _______.

discrete

To find the mean from a frequency​ distribution, calculate the weighted mean by using the class​ ______________ as weights.

freqencies

​A(n) ____________________ is a graph that plots the class midpoints on the horizontal axis against the class frequencies on the vertical​ axis, and then connects the points with the line segments.

frequency polygon

​A(n) ____________________ is a bar graph in which the height of each rectangle is the frequency or relative frequency of the class. The width of each rectangle is the​ same, and the rectangles touch each other.

histogram

A variable is at the ____ level of measurement if it allows for the values of the variable to be arranged in a specific order and the difference between any two values is meaningful, but the ratio is not.

interval

The _____ is found by adding all the data values and dividing by the total number of values.

mean

The coefficient of variation describes the standard deviation relative to the _____ and is expressed as a _____.

mean, percent

When an odd number of data values are arranged in order, the ____ is the middle value

median

If the maximum and minimum values in a data set are​ averaged, the result is the​ __________.

midrange

The data value that occurs with the greatest frequency is called the​ ___________.

mode

When comparing two populations with the same variable of interest in the same unit of​ measure, the larger the standard​ deviation, the​ _____________ dispersion there is in the distribution.

more

A variable is at the​ _______ level of measurement if the values of the variable​ name, label, or categorize.

nominal

A frequency distribution lists the​ _________ of occurrences of each category of​ data, while a relative frequency distribution lists the​ _________ of occurrences of each category of data.

number , proportion

Do people walk faster in an airport when they are departing​ (getting on a​ plane) or after they have arrived​ (getting off a​ plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed​ (in feet per​ minute) of each. What type of study design is being​ performed?

observational study

A variable is at the​ _______ level of measurement if it allows for the values of the variable to be arranged in a specific order but the differences between values either cannot be determined or are meaningless.

ordinal

Fill in the blank to complete the statement below. A​ _________________ is a numerical measurement describing some characteristic of a population.

parameter

The​ _________________ is/are the entire group of individuals or items being studied.

population

In a ___ study, data are collected in the future from cohorts which share common factors.

prospective study

A​ ________________ variable classifies individuals based on some attribute or characteristic.

qualitative

A​ ________________ variable counts or measures something and has numeric values.

quantitative

A variable is at the ____ level of measurement if it allows for the values of the variable to be arranged in a specific order and both differences and ratios of values have meaning.

ratio

A study that requires individuals to look back in time or requires the researcher to look at existing records is considered​ _______.

retrospective

What is the symbol used to represent the sample standard​ deviation?

s

What is the symbol used to represent the sample variance?

s2 (s squared)

The​ _________________ is/are a subset of the population that is being studied.

sample

Suppose that a researcher is interested in the average standardized test score for fifth graders in a local school district. The fifth graders at a specific school would comprise a​ ___________ and their average test score would be a​ ___________.

sample; statistic

The interquartile range​ (IQR) is a measure of the​ ____________ of the middle​ ____________ percent of the data.

spread; 50

A​ z-score represents how many​ ______________ a data value is above or below the​ ______________.

standard deviations; mean

A​ _________________ is a numerical measurement describing some characteristic of a sample.

statistic

A​ __________ sample is obtained by dividing the population into homogenous groups and randomly selecting individuals from each group.

stratified

Fill in the blank to complete the statement below. A​ __________ sample is obtained by randomly selecting an individual and then selecting every kth individual from the population after the first one.

systematic

The interquartile range​ (IQR) is the difference between the​ _______ quartile and the​ _______ quartile.

third; first

When plotting an​ ogive, the​ x-coordinates of the points are equal to the​ __________________ of each class.

upper limits

Which two graphs allow the reader to retrieve the original list of​ data?

​Stem-and-leaf plots and dotplots

What is a placebo and what purpose does it serve in an experiment?

A placebo is a fake treatment that looks like the treatment being tested in the experiment. Placebos blind subjects so they do not know whether or not they are receiving the treatment.

Explain the difference between a bar graph and a Pareto chart. Choose the correct answer below. A. A Pareto chart is a particular type of bar graph in which the bars are drawn in decreasing order of height. B. A bar graph is used for qualitative​ data, and a Pareto chart is used for quantitative data. C. A Pareto chart is always drawn with vertical​ bars, while a bar graph can be horizontal or vertical. D. A Pareto chart is a particular type of bar graph in which the bars are touching and all the same width.

A. A Pareto chart is a particular type of bar graph in which the bars are drawn in decreasing order of height.

Explain why Social Security Number is considered a qualitative variable even though it contains numbers. Choose the correct answer below. A. Addition and subtraction of Social Security Numbers does not provide meaningful results. This makes it qualitative even though it is numeric. B. Since Social Security Number is a variable at the interval level of​ measurement, it must be qualitative rather than quantitative. C. Social Security Number is a qualitative variable since there are an infinite number of possible values that are not countable. D. Social Security Number is a qualitative variable since there are a finite or countable number of values.

A. Addition and subtraction of Social Security Numbers does not provide meaningful results. This makes it qualitative even though it is numeric.

Suppose you construct a graph to compare the student populations of the five largest high schools in your city and choose to depict the populations with school buildings of various sizes. If the school buildings are drawn so that the length and the width are each in proportion to the population of the corresponding​ schools, is the resulting graph​ misleading? Why or why​ not? Choose the correct answer below. A. The graph will be misleading since the student populations are​ one-dimensional data, but the graph uses a​ two-dimensional school building to represent it. B. The graph will be misleading since pictures cannot be used to represent data. C. The graph will not be misleading since the areas of the school buildings are in proportion to the population of the corresponding schools. D. The graph will not be misleading since the school building picture being used is related to the school population data.

A. The graph will be misleading since the student populations are​ one-dimensional data, but the graph uses a​ two-dimensional school building to represent it.

​Suppose, on the warmest day of the​ month, the daily high temperature in a city is accidentally recorded as 700 instead of 70 degrees Fahrenheit. Compare the effect this mistake will have on the mean monthly high temperature to the effect on the median monthly high temperature. Choose the correct answer below. A. The mean will increase​ significantly, but the median will not change as a result of the mistake. B. The median will increase​ significantly, but the mean will not change as a result of the mistake. C. The mean and median will both increase significantly as a result of the mistake. D. Neither the mean nor the median will increase as a result of the mistake.

A. The mean will increase​ significantly, but the median will not change as a result of the mistake.

Which measure of center​ (mean or​ median) is​ resistant? Explain what it means for that measure to be resistant. Choose the correct answer below. A. The median is resistant because it is not sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the median would not change since that largest value does not factor into its computation. B. The mean is resistant because it is sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the mean would change since that largest value factors into its computation. C. The mean is resistant because it is not sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the mean would not change since that largest value does not factor into its computation. D. The median is resistant because it is sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the median would change since that largest value factors into its computation.

A. The median is resistant because it is not sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the median would not change since that largest value does not factor into its computation.

What is the symbol used to represent the population standard​ deviation? A. sigma B. s C. mu D. x overbar

A. sigma

A company advertises a mean lifespan of 1000 hours for a particular type of light bulb. If you were in charge of quality control at the​ factory, would you prefer that the standard deviation of the lifespans for the light bulbs be 5 hours or 50​ hours? Why? Choose the correct answer below. A. 5 hours would be preferable since a smaller standard deviation indicates a longer average lifespan for the light bulbs. B. 5 hours would be preferable since a smaller standard deviation indicates more consistency. C. 50 hours would be preferable since a larger standard deviation indicates a longer average lifespan for the light bulbs. D. 50 hours would be preferable since a larger standard deviation indicates more consistency.

B. 5 hours would be preferable since a smaller standard deviation indicates more consistency.

Which distribution shape​ (skewed left, skewed​ right, or​ symmetric) is most likely to result in the mean being substantially smaller than the​ median? Choose the correct answer below. A. A distribution that is skewed right will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the right. B. A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left. C. A symmetric distribution will likely have a mean that is smaller than the median since the median is more resistant to extreme values than the mean. D. There is no way to predict the relationship between the mean and median based on the shape of the distribution. Question is complete.

B. A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left.

What is an advantage to using a​ stem-and-leaf plot instead of a histogram to display​ data? Choose the correct answer below. A. A​ stem-and-leaf plot shows the shape of the distribution while the histogram does not. B. A​ stem-and-leaf plot allows for retrieval of the original data from the plot while the histogram does not. C. A​ stem-and-leaf plot is often much faster to create than a​ histogram, especially for large data sets. D. These are all advantages of a​ stem-and-leaf plot over a histogram.

B. A​ stem-and-leaf plot allows for retrieval of the original data from the plot while the histogram does not.

Suppose a pediatrician is wondering whether there is more variability in the heights or weights of the​ 2-year-old boys that he sees and collects the data below for a sample of 100​ 2-year-old boys in his practice. He concludes that the​ boys' weights vary more than their heights since the standard deviation is greater for weight than for height. What is wrong with this​ conclusion? ​Heights: mean =30.2 in., standard deviation = 1.9 in. ​Weights: mean =29.4 lb, standard deviation = 2.1 lb Choose the correct answer below. A. Since the standard deviation is larger for the​ weights, the weights actually vary less than the heights. B. Since the standard deviations have different​ units, he cannot compare them directly. The coefficient of variation should be used instead. C. In order to compare the​ variability, he would need to calculate the variance instead of the standard deviation. D. Nothing is wrong with his conclusion. Since the heights and weights have equal​ means, it is perfectly valid to compare the standard deviations to decide which data has more variability.

B. Since the standard deviations have different​ units, he cannot compare them directly. The coefficient of variation should be used instead.

If all the data values in a population are converted to​ z-scores, the distribution of​ z-scores will have what​ mean? Choose the correct answer below. A. The mean of the​ z-scores cannot be determined. B. The mean of the​ z-scores will be zero. C. The mean of the​ z-scores will be the same as the mean of the original distribution of data. D. The mean of the​ z-scores will be one.

B. The mean of the​ z-scores will be zero.

How can you tell from a boxplot if the distribution is​ symmetric? Choose the correct answer below. A. It is not possible to determine the shape of the distribution from a boxplot. B. The median is in the center of the​ box, and the left and right whiskers are approximately the same length. C. The median is in the center of the box. D. The left and right whiskers are approximately the same length.

B. The median is in the center of the​ box, and the left and right whiskers are approximately the same length.

If​ someone's gross annual income has a​ z-score of positive​ 2, what can be​ concluded? Choose the correct answer below. A. Their income is 2 standard deviations above the median income. B. Their income is 2 standard deviations above the mean income. C. Their income is twice the mean income. D. Their income is 2 standard deviations below the median income.

B. Their income is 2 standard deviations above the mean income.

Suppose you want to calculate the​ z-score for your height. How will the​ z-scores compare if you use your height in inches verses​ centimeters? Choose the correct answer below. A. If you use your height in​ inches, the​ z-score will be larger since an inch is larger than a centimeter. B. The​ z-scores will be the same regardless of the unit used for your height because​ z-scores are unitless. C. The​ z-scores will be different based on the unit used for​ height, but it is not possible to predict which will yield a larger​ z-score. D. If you use your height in​ inches, the​ z-score will be smaller since you are measuring it in a larger unit. Question is complete.

B. The​ z-scores will be the same regardless of the unit used for your height because​ z-scores are unitless

What is the symbol used to represent the sample​ mean? Choose the correct answer below. A. sigma B. x overbar C. mu D. s

B. x overbar

What is the symbol used to represent the population​ mean? Choose the correct answer below. A. s B. mu C. x overbar D. sigma

B. mu

Suppose your statistics professor teaches two sections of your course this semester. She gives the same exam to each class. Their performance is summarized below. Can she conclude that the overall mean on the exam was 80​ (the average of the two individual class​ means)? Why or why​ not? First​ Class: n=32 mean= 75 standard deviation = 5.6 Second Class: n=38 mean= 85 standard deviation = 7.2 Choose the correct answer below. A. Yes. The two means can be averaged as long as the classes took the same exam. B. Yes. The two means can be averaged as long as each class is considered a simple random sample. C. No. Since the classes have different standard deviations on the​ exam, she cannot average the means. D. No. Since the class sizes are​ different, she would need to find the weighted mean.

D. No. Since the class sizes are​ different, she would need to find the weighted mean.

Explain why the mean should not be found for a sample of zip codes. Which measure of center should be used​ instead? Choose the correct answer below. A. Zip codes are quantitative​ data, but are at the ordinal level of measurement. Since they cannot be added in a meaningful​ way, the mean cannot be found. The median should be used instead. B. Zip codes are quantitative​ data, but are at the ordinal level of measurement. Since they cannot be added in a meaningful​ way, the mean cannot be found. The mode should be used instead. C. Even though they are numeric​ data, zip codes are qualitative since they do not measure or count anything. The mean cannot be found since adding zip codes would be meaningless. For qualitative​ data, the mode is the only measure of center that can be found. D. Even though they are numeric​ data, zip codes are qualitative since they do not measure or count anything. The mean cannot be found since adding zip codes would be meaningless. For qualitative​ data, the median is the only measure of center that can be found.

C. Even though they are numeric​ data, zip codes are qualitative since they do not measure or count anything. The mean cannot be found since adding zip codes would be meaningless. For qualitative​ data, the mode is the only measure of center that can be found.

When reporting the mean or standard​ deviation, the result is usually rounded to how decimal​ places? Choose the correct answer below. A. The same number of decimal places as is present in the original data B. Two more decimal places than is present in the original data C. One more decimal place than is present in the original data D. One fewer decimal places than is present in the original data

C. One more decimal place than is present in the original data

A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. What is the relationship between the mean and the median for this​ data? Choose the correct answer below. A. The mean will be substantially smaller than the median since the distribution is skewed left. B. The mean and median will be roughly equal since the distribution is fairly symmetric. C. The mean will be substantially larger than the median since the distribution is skewed right. D. The mean will be substantially smaller than the median since the distribution is skewed right. Your answer is not correct.

C. The mean will be substantially larger than the median since the distribution is skewed right. see pic

What is wrong with the following class limits for organizing weight data for a sample of 200 adult men in the United​ States? ​140-150 pounds ​150-160 pounds ​160-170 pounds ​170-180 pounds ​180-190 pounds ​190-200 pounds ​200-210 pounds ​210-220 pounds ​220-230 pounds

Classes are overlapping.

If the effect of two factors on the response variable cannot be​ distinguished, what can be concluded about the​ experiment? Choose the correct answer below. A. There has been a placebo effect in the experiment. B. Blinding was not used in the experiment. C. There is a lurking variable in the experiment. D. Confounding has occurred in the experiment.

D. Confounding has occurred in the experiment.

What must be true for a sample to be considered a simple random​ sample? Choose the correct answer below. A. Every member​ (or sample) of the population must have a known probability of being selected. B. Every individual member of the population must be selected. C. Every member​ (or sample) of the population must have a different probability of being selected. D. Every member​ (or sample) must have the same chance of being selected as every other member​ (or sample of the same​ size).

D. Every member​ (or sample) must have the same chance of being selected as every other member​ (or sample of the same​ size).

Suppose every student in a class is surveyed and it is found that​ 75% of the class plans to take another math class. It is reported that​ 75% of all students at the school plan to take another math class. Is this an example of descriptive or inferential​ statistics? Explain. Choose the correct answer below. A. Descriptive​ statistics; the results of the class sample are described without making any generalizations about the population of all students at the school. B. Descriptive​ statistics; the results of the class sample are extended to make a generalization about the population of all students at the school. C. Inferential​ statistics; the results of the class sample are described without making any generalizations about the population of all students. D. Inferential​ statistics; the results of the class sample are extended to make a generalization about the population of all students at the school.

D. Inferential​ statistics; the results of the class sample are extended to make a generalization about the population of all students at the school.

A collection of data on class sizes at a community college produces the​ five-number summary below. Comment on the shape of the distribution of class sizes. Min = 12 Upper Q 1 = 22 Upper Q 2 = 35 Upper Q 3= 38 Max = 40 Choose the correct answer below. A. The distribution appears to be skewed right since the median is further from the first quartile than the third quartile.​ Also, the left whisker would be longer than the right whisker in a boxplot for the data. B. The distribution appears to be fairly symmetric since the median is about the same distance from the first and third quartiles. C. The distribution appears to be skewed left since the median is closer to the first quartile than the third quartile.​ Also, the right whisker would be longer than the left whisker in a boxplot for the data. D. The distribution appears to be skewed left since the median is further from the first quartile than the third quartile.​ Also, the left whisker would be longer than the right whisker in a boxplot for the data.

D. The distribution appears to be skewed left since the median is further from the first quartile than the third quartile.​ Also, the left whisker would be longer than the right whisker in a boxplot for the data.

Which statement is NOT true regarding the​ mean? Choose the correct answer below. A. The calculation of the mean uses all the values in the data set. Your answer is not correct. B. The mean should be used when the distribution is roughly symmetric. C. The mean is the center of gravity or balancing point for the data set. D. The mean is always the best measure of center.

D. The mean is always the best measure of center.

If a professor adds 10 points to each​ student's final exam​ score, how will it affect the class mean on the final​ exam? Choose the correct answer below. A. The mean will not change. B. The mean will increase by less than 10 points. C. The mean will increase by more than 10 points. D. The mean will increase by 10 points.

D. The mean will increase by 10 points.

How can you tell from a boxplot if the distribution is skewed​ right? Choose the correct answer below. A. The median is to the right of the center of the​ box, and the left whisker is substantially longer than the right whisker. B. The median is to the right of the center of the​ box, and the right whisker is substantially longer than the left whisker. C. The median is to the left of the center of the​ box, and the left whisker is substantially longer than the right whisker. D. The median is to the left of the center of the​ box, and the right whisker is substantially longer than the left whisker.

D. The median is to the left of the center of the​ box, and the right whisker is substantially longer than the left whisker.

What is the symbol used to represent the population​ variance? A. sigma B. s squared C. s D.sigma squared

D.sigma squared

Suppose every student in a class is surveyed and it is reported that​ 75% of the class plans to take another math class. Is this an example of descriptive or inferential​ statistics? Explain.

Descriptive​ statistics; The results of the class sample are described without making any generalizations about the population of all students at the school.

Suppose a newspaper surveys 250 adults in a neary town and inquires about their cell phone carrier. The accompanying table summarizes the results. Does this table describe a relative frequency distribution? Why or why not?

No. The sum of the relative frequencies is 95% not 100%

Suppose a student earns a 75 on his statistics​ exam, and his grade has a​ z-score of 1.5. Since the class did not perform well on the​ exam, the professor announces that she will adjust the grades by adding 10 points to each score. How will this adjustment change the​ student's z-score?

Your​ z-score will not change since the adjustment shifts the entire distribution of scores but does not change the relative position of your score in the class.

Suppose a pharmaceutical company is designing a​ double-blind experiment to test their new allergy medication. They divide the 200 subjects by gender and then randomly assign the men and women to either receive the medication or a placebo. The researcher finds that even the group receiving the placebo​ (a sugar​ pill) showed a decrease in allergy symptoms. Which of the following accounts for this​ result? Choose the correct answer below. Blocking Confounding Placebo effect Response bias

Placebo effect

What purpose does replication serve in an​ experiment?

Replication insures that the effect of a treatment is not due to some characteristic of a single experimental unit.

An ogive will always end at a point whose y-coordinate is the ____

Sample size

Which of the statements below is true concerning bar graphs?

The height of each bar represents the category's frequency or relative frequency.

A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. What is the relationship between the mean and the median for this​ data?

The mean and median will be roughly equal since the distribution is fairly symmetric.

If all the data values in a set are identical what can you conclude about the standard deviation?

The standard deviation is zero.

A company was conducting a survey to investigate​ people's spending habits and how they may have changed in recent years. One question on the survey​ was, "Did you spend​ more/less/the same amount of money this year as you did in​ 2007, the year the recession began in earnest in this​ country?" Is this question​ biased? If​ so, what answer does it​ favor?

This question is biased toward​ "spend less," since it mentions the recent recession. Many people would feel that they should answer that they spent​ less, since the country is in a recession.

True or False? A histogram and a relative frequency histogram constructed from the same data always have the same basic shape.

True. A relative frequency histogram will have a different scale on the y-axis but the same shape as a regular histogram.