# Math 221 - Chapter 2

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question
Fill in the blank below. Theâ€‹ _____ organizes data by recording all the values observed in a sample as well as how many times each value was observed.
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 dataâ€‹ set, it is called the distribution of the sample.
question
Whatâ€‹ two-step process is used to examineâ€‹ 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
B. See the data and summarize it note: When examining aâ€‹ distribution, first visualize or see theâ€‹ distribution, then use characteristics of the visualization to summarize the data.
question
All methods used for visualizing distributions are based on which of theâ€‹ 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.
A. Make a mark that indicates how many times each value occurred in the data set. note: When visualizing aâ€‹ distribution, the idea is to make some sort of mark that indicates how many times each value occurs in the data set.
question
In aâ€‹ histogram, observations are grouped into intervals calledâ€‹ ____.
Answer: bins note: Histograms produce a smooth graphic by grouping observations into intervals called bins.
question
Changing the width of bins in a histogramâ€‹ _______.
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 ofâ€‹ detail, while wider bins will hide more detail.
question
"Relative frequency" is the same as which of theâ€‹ following? Choose the correct answer below. Bin width Proportion Frequency histogram Distribution
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 followingâ€‹ 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
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 numericalâ€‹ data, which of the following is not a feature that needs to beâ€‹ considered? Choose the correct answer below. Shape Each individual value Center Spread
answer: Each individual value note: When examining distributions of numericalâ€‹ data, pay attention to theâ€‹ 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 numericalâ€‹ data, which of the following is not one of the three basic characteristics of aâ€‹ 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.
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 aâ€‹ distribution's shape. The three basic characteristics of aâ€‹ distribution's shape are whether the distribution is symmetric orâ€‹ skewed, the number of mounds that appear in theâ€‹ 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 calledâ€‹ ________.
Answer: right-skewed note: Aâ€‹ 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 typicalâ€‹ week, what shape would the data distribution be expected toâ€‹ have? Choose the correct answer below. â€‹Right-skewed Symmetric â€‹Left-skewed Bimodal
Answer: right-skewed note: The smallest possible value for this data set isâ€‹ 0, and most values will likely cluster around a common value.â€‹ However, the presence of a small number of people who watch a great deal of TV would cause the distribution to beâ€‹ right-skewed
question
The existence of multiple mounds in a distribution is sometimes a sign of which of theâ€‹ 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
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. Forâ€‹ example, if a group that has aâ€‹ right-skewed distribution were combined with a group that has aâ€‹ 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 calledâ€‹ what? Choose the correct answer below. Skewed Variables Outliers None of the above
Outliers note: When values are so large or so small that they do not fit into the pattern of theâ€‹ distribution, these extreme values are called outliers.
question
The dotplot shows the body mass indexâ€‹ (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 thatâ€‹ 3% of people from the country were morbidly obese.
a. From the peopleâ€‹ surveyed, how many people would be considered morbidlyâ€‹ 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 9â€‹%. â€‹(Round to the nearest whole number asâ€‹ 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 architectâ€‹ Vitruvius, aâ€‹ person's armspanâ€‹ (the distance from fingertip to fingertip with the arms stretchedâ€‹ wide) is approximately equal to his or her height. Forâ€‹ example, people 5 feet tall tend to have an armspan of 5 feet.â€‹ 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 theirâ€‹ 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.
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 differentâ€‹ "typical" heights of men and women.
question
What are two commonly used graphs to display the distribution of a sample of categoricalâ€‹ data? Choose the correct answer below. Bar graph and pie chart Histograms and dotplots Dotplots and bar graphs Bar graph and stemplot
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 Paretoâ€‹ 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
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 andâ€‹ histograms? Choose the correct answer below. A. In a barâ€‹ chart, itâ€‹ doesn't matter how wide or narrow the bars are. B. In a barâ€‹ chart, sometimes the order in which you place the barsâ€‹ doesn't matter. C. A bar chart is used for numerical variables while a histogram is used for categorical variables. D. In a barâ€‹ chart, there are gaps between the bars.
C. A bar chart is used for numerical variables while a histogram is used for categorical variables. note: Bar charts are used for categoricalâ€‹ 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 theâ€‹ wedge-shaped slice of a pieâ€‹ chart, which of the following is true of pieâ€‹ 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.
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 betweenâ€‹ wedge-shaped slices on a chart.
question
When describing the distribution of a categoricalâ€‹ variable, the category that appears most often is called theâ€‹ _____.
mode note: When describing the distribution of a categoricalâ€‹ variable, the category that appears most often is called the mode.
question
A categorical variable is only called bimodal under whatâ€‹ 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.
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 categoricalâ€‹ distribution, it is sometimes useful to think of the wordâ€‹ _______. mode shape diversity center
note: If the distribution of a categorical variable has a lot ofâ€‹ diversity, or many observations in many differentâ€‹ categories, then the variability is high. If the distribution has only a littleâ€‹ diversity, or many of the observations fall into the sameâ€‹ category, then the variability is low.
question
When summarizing graphs of categoricalâ€‹ data, report theâ€‹ _______ and describe theâ€‹ _______.