Math 221 - Chapter 2

7 September 2022
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question
Fill in the blank below. The‚Äč _____ organizes data by recording all the values observed in a sample as well as how many times each value was observed.
answer
Answer: distribution of a sample note: When the values from a data set are organized with the number of times each value appeared in the data‚Äč set, it is called the distribution of the sample.
question
What‚Äč two-step process is used to examine‚Äč distributions? A. See the data and graph it B. See the data and summarize it C. Gather the data and graph it D. Gather the data and analyze it
answer
B. See the data and summarize it note: When examining a‚Äč distribution, first visualize or see the‚Äč distribution, then use characteristics of the visualization to summarize the data.
question
All methods used for visualizing distributions are based on which of the‚Äč following? Choose the correct answer below. A. Make a mark that indicates how many times each value occurred in the data set. B. Make a histogram of the data. C. Pick a graph and summarize the data using that graph. D. Make a dotplot of the data.
answer
A. Make a mark that indicates how many times each value occurred in the data set. note: When visualizing a‚Äč distribution, the idea is to make some sort of mark that indicates how many times each value occurs in the data set.
question
In a‚Äč histogram, observations are grouped into intervals called‚Äč ____.
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Answer: bins note: Histograms produce a smooth graphic by grouping observations into intervals called bins.
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Changing the width of bins in a histogram‚Äč _______.
answer
Answer: changes the shape of the histogram. note: Changing the width of the bins in a histogram changes the shape of the histogram. Narrow bins will result in a spiky histogram that shows a lot of‚Äč detail, while wider bins will hide more detail.
question
"Relative frequency" is the same as which of the‚Äč following? Choose the correct answer below. Bin width Proportion Frequency histogram Distribution
answer
Answer: proportion note: A relative frequency is the proportion of the observations that exhibit the relevant characteristic.
question
A stemplot is often useful in which of the following‚Äč cases? Choose the correct answer below. A. When technology is not available and the data set is not large B. When the data has already been summarized in a histogram C. When the data set is large and technology is available to make the stemplot D. When technology is not available and the data set is large
answer
A. When technology is not available and the data set is not large note: A stemplot is useful for visualizing numerical variables when technology is not available and the data set is not large. They are also useful to be able to easily see the actual values of the data.
question
When examining a distribution of numerical‚Äč data, which of the following is not a feature that needs to be‚Äč considered? Choose the correct answer below. Shape Each individual value Center Spread
answer
answer: Each individual value note: When examining distributions of numerical‚Äč data, pay attention to the‚Äč shape, center, and spread. Each individual value is not an important feature of a distribution of numerical data.
question
When examining the shape of a distribution of numerical‚Äč data, which of the following is not one of the three basic characteristics of a‚Äč distribution's shape? Choose the correct answer below. A. Whether the distribution is symmetric or skewed. B. Whether any unusually large or small values are present. C. How many numbers are in the data set. D. How many mounds appear.
answer
C. How many numbers are in the data set. note: The amount of numbers in a data set is not one of the three basic characteristics of a‚Äč distribution's shape. The three basic characteristics of a‚Äč distribution's shape are whether the distribution is symmetric or‚Äč skewed, the number of mounds that appear in the‚Äč distribution, and whether any unusually large or small values are present.
question
Fill in the blank below. A distribution of a variable in which most of the values are relatively small but that also has a few very large values is called‚Äč ________.
answer
Answer: right-skewed note: A‚Äč right-skewed distribution has mostly values that are relatively small but also has a few very large values. This makes the graphical representation of the graph appear to have a tail that extends to the right.
question
Question Help If a sample of people were asked how many hours of TV they watched in a typical‚Äč week, what shape would the data distribution be expected to‚Äč have? Choose the correct answer below. ‚ÄčRight-skewed Symmetric ‚ÄčLeft-skewed Bimodal
answer
Answer: right-skewed note: The smallest possible value for this data set is‚Äč 0, and most values will likely cluster around a common value.‚Äč However, the presence of a small number of people who watch a great deal of TV would cause the distribution to be‚Äč right-skewed
question
The existence of multiple mounds in a distribution is sometimes a sign of which of the‚Äč following? Choose the correct answer below. A. The data is not from a random sample B. Two very different groups have been combined into a single collection C. The graph of the distribution was drawn incorrectly D. All the values in the data are centered around one typical value
answer
B. Two very different groups have been combined into a single collection note: Sometimes, the presence of multiple mounds can indicate that there have been multiple groups combined into a single sample. For‚Äč example, if a group that has a‚Äč right-skewed distribution were combined with a group that has a‚Äč left-skewed distribution, the result would be a sample that has two mounds.
question
Values so large or so small that they do not fit into the pattern of the distribution are called‚Äč what? Choose the correct answer below. Skewed Variables Outliers None of the above
answer
Outliers note: When values are so large or so small that they do not fit into the pattern of the‚Äč distribution, these extreme values are called outliers.
question
The dotplot shows the body mass index‚Äč (BMI) for 137 randomly surveyed people from a certain country. a. A BMI of more than 40 is considered morbidly obese. Report the number of morbidly obese shown in the dotplot. b. Report the percentage of people who are morbidly obese. Compare this with a recent estimate that‚Äč 3% of people from the country were morbidly obese.
answer
a. From the people‚Äč surveyed, how many people would be considered morbidly‚Äč obese? The number of people considered morbidly obese is 12. b. Find the percentage of people from the survey who are morbidly obese. The percentage of people considered morbidly obese is about 9‚Äč%. ‚Äč(Round to the nearest whole number as‚Äč needed.) Compare the survey value with the estimate given. The percentage of morbidly obese people in the survey is greater than the estimated percentage of people that are considered morbidly obese.
question
According to the ancient Roman architect‚Äč Vitruvius, a‚Äč person's armspan‚Äč (the distance from fingertip to fingertip with the arms stretched‚Äč wide) is approximately equal to his or her height. For‚Äč example, people 5 feet tall tend to have an armspan of 5 feet.‚Äč Explain, then, why the distribution of armspans for a class containing roughly equal numbers of men and women might be bimodal. Select the correct answer below. A. Some students will have an armspan less than their‚Äč height, and some students will have an armspan greater than their height. B. The class could meet at different times on different days. C. Men and women tend to have different heights and therefore different armspans. Your answer is correct. D. There is no reason why the distribution might be bimodal.
answer
Men and women tend to have different heights and therefore different armspans. note: Recall that a bimodal distribution as two distinct mounds. The two mounds are created by the different‚Äč "typical" heights of men and women.
question
What are two commonly used graphs to display the distribution of a sample of categorical‚Äč data? Choose the correct answer below. Bar graph and pie chart Histograms and dotplots Dotplots and bar graphs Bar graph and stemplot
answer
Bar graph and pie chart note: Two commonly used graphs to display the distribution of a sample of categorical data are bar charts and pie charts.
question
What are Pareto‚Äč charts? Choose the correct answer below. A. Bar charts that are sorted from most frequent to least frequent B. Bar charts that are sorted from least frequent to most frequent C. Histograms that are sorted from least frequent to most frequent D. Dotplots that are sorted from most frequent to least frequent
answer
A. Bar charts that are sorted from most frequent to least frequent note: A Pareto chart is a bar chart that is sorted from most frequent to least frequent.
question
Which of the following is not a difference between bar charts and‚Äč histograms? Choose the correct answer below. A. In a bar‚Äč chart, it‚Äč doesn't matter how wide or narrow the bars are. B. In a bar‚Äč chart, sometimes the order in which you place the bars‚Äč doesn't matter. C. A bar chart is used for numerical variables while a histogram is used for categorical variables. D. In a bar‚Äč chart, there are gaps between the bars.
answer
C. A bar chart is used for numerical variables while a histogram is used for categorical variables. note: Bar charts are used for categorical‚Äč variables, while histograms are used for numerical variables.
question
Because the human eye has a difficult time judging how much area is taken up by the‚Äč wedge-shaped slice of a pie‚Äč chart, which of the following is true of pie‚Äč charts? Choose the correct answer below. A. Pie charts are only used for small data sets. B. Pie charts are not commonly used by statisticians or in scientific settings. Pie charts are preferred over bar graphs. D. Pie charts are only used if they are made by a computer.
answer
B. Pie charts are not commonly used by statisticians or in scientific settings. note: Pie charts are not commonly used by statisticians or in scientific settings because it is difficult to judge the difference between‚Äč wedge-shaped slices on a chart.
question
When describing the distribution of a categorical‚Äč variable, the category that appears most often is called the‚Äč _____.
answer
mode note: When describing the distribution of a categorical‚Äč variable, the category that appears most often is called the mode.
question
A categorical variable is only called bimodal under what‚Äč circumstances? Choose the correct answer below. A. Two categories are nearly tied for most frequent outcomes. The data consists of exactly two categories. C. One category occurs more frequently than any other. D. Two categories have exactly the same frequency.
answer
A. Two categories are nearly tied for most frequent outcomes. note: A categorical variable is only called bimodal if two categories are nearly tied for most frequent outcomes.
question
Fill in the blank below. When thinking about the variability of a categorical‚Äč distribution, it is sometimes useful to think of the word‚Äč _______. mode shape diversity center
answer
note: If the distribution of a categorical variable has a lot of‚Äč diversity, or many observations in many different‚Äč categories, then the variability is high. If the distribution has only a little‚Äč diversity, or many of the observations fall into the same‚Äč category, then the variability is low.
question
When summarizing graphs of categorical‚Äč data, report the‚Äč _______ and describe the‚Äč _______.
answer
When summarizing graphs of categorical‚Äč data, report the mode(s) and describe the variability. note: When describing a distribution of categorical‚Äč data, the mode should be mentioned and something should be said about the variability.
question
What is the first step in almost every investigation of‚Äč data? Choose the correct answer below. A. Describe the variability. B. Make an appropriate graph. Your answer is correct. C. Determine if the data contain any outliers. D. Determine the center.
answer
note: The first step in every investigation of data is to make an appropriate graph.
question
2.5.RA-2 Question Help What is the most common trick to mislead readers of bar‚Äč graphs? Choose the correct answer below. A. Change the width of the bars to make some categories appear more important than others. B. Change the scale of the horizontal axis so that it does not start at 0. C. Change the scale of the vertical axis so that it does not start at 0. Your answer is correct. D. Change the color of the bars to make some categories appear more important than others.
answer
note: By changing the vertical axis so that it does not start at‚Äč 0, minor differences in the heights of the bars can be exaggerated to look very significant.
question
correct, 2.5.RA-3 Question Help Which of the following is not a way in which the Internet is influencing statistical‚Äč graphics? Choose the correct answer below. A. Allowing for a greater variety of graphical displays B. Decreasing the use of misleading graphics Your answer is correct. C. Increasing the use of interactive displays D. None of the above
answer
note: The Internet is not decreasing the use of misleading graphics.