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When transforming a dataset into a stemplot, first rearrange the numbers into ascending order. The stem is everything except the right most digit. The leaf is the most-right digit. What is the correct representation of a stemplot for this dataset?
40, 42, 45, 46, 53, 54, 22, 57, 63, 22, 25
Correct! The first digit of each number is the stem, without repeating that number. Great job!...
Read MoreWhen transforming a dataset into a stemplot, first rearrange the numbers into ascending order. The stem is everything except the right most digit. The leaf is the most-right digit. For instance, the #12 means the stem is the 1 and the leaf is the 2. In the following series of numbers, which digits are the stems, in proper order?
40, 42, 45, 46, 53, 54, 22, 57, 63, 22, 25
2, 4, 5, 6Correct! You rearrange the numbers in ascending order and then take the first digit of each one as the stem; you do not repeat this number. Good work!...
Read MoreWhat percentage of the rats navigated the maze in less than 5.5 minutes?
Here again is the histogram showing the distribution of times, in minutes, required for 25 rats in an animal behavior experiment to navigate a maze successfully.
For the data described by the above histogram,
Here again is the histogram showing the distribution of times, in minutes, required for 25 rats in an animal behavior experiment to navigate a maze successfully.
A possible value of the median in this example is:
Here again is the histogram showing the distribution of times, in minutes, required for 25 rats in an animal behavior experiment to navigate a maze successfully.
Assume that the largest observation in this dataset is 8.6 minutes. If this observation were wrongly recorded as 86, then:
84%Good job! From the histogram we can find that 3 + 8 + 6 + 4 = 21 out of the 25 rats fall below 5.5 minutes (first four bars). Since the question asks about the percentage of observations, the answer is 21/25 * 100 = 84%Q2This information is not provided by the histogramQ3Which of the following be...
Read MoreAt the beginning of the semester, an Intro to Statistics instructor asked the 225 students enrolled in the class to complete a survey. For each student, the instructor collects information about the following:
Sport (Favorite sport: Football, Baseball, Basketball, Hockey, Other)
Exercise (How many minutes do you spend exercising per week)
Personality (on a 0-25 scale, how would you describe your personality 0=total introvert, 25=total extrovert)
Death penalty (Strongly agree, Agree, Neutral, Disagree, Strongly Disagree)
Question 1 of 6The students enrolled in Intro to StatisticsCorrect. Individuals are the people/objects that information is collected on. Therefore, in this case, the individuals are the 225 students enrolled in the Intro to Statistics course.Question 2 of 64Correct. The variables are the characteris...
Read MoreAnother example:
In general, the larger the animal the longer the length of pregnancy (also called gestation period). For the horse, for example, the gestation period varies roughly according to a normal distribution with a mean of 336 days and a standard deviation of 3 days. (Source: These figures are from Moore and McCabe, Introduction to the Practice of Statistics.) Use the Standard Deviation Rule to answer the following questions: (a picture of the SD rule applied to this distribution will help).
Almost all (99.7%) horse pregnancies fall in what range of lengths?Between 327 and 345 daysGood job! The Standard Deviation Rule tells us that virtually all the data fall within 3 standard deviations of the mean, which in this case is exactly between 336 - 3(3) = 327, and 336 + 3(3) = 345.What perce...
Read MoreIn the previous activity, we compared the distributions of the number of wins of teams in two Division I conferences. When comparing distributions using side-by-side boxplots you can also compare more than two groups. The following image compares the distributions of the number of football game wins of teams in five Division I conferences in the 2014 season.
X axis is labeled "Football Wins 2014." ACC Boxplot: box spans ~6 to ~9; lower line extends from 3 to ~6; uppline extends from ~9 to ~13. Big 10 Boxplot: box spans 5 to 9.5; lower line extends from 3 to 5; upper line extends from 9.5 to 14. Pac 12 Boxplot: box spans ~5 to 10; lower line extends from 2 to ~5; uppline extends from 10 to ~13. SEC boxplot: box spans 7 to 10; lower line extends from 3 to 7; upper line extends from 10 to 12. Con USA Boxplot: box spans 4 to 8; lower line extends from 3 to 4; upper line extends from 8 to ~13.
Which of the five conferences had the larger percentage of teams with eight or more wins?
Pac 12Good Job! Indeed, since 8 is between Q1 and the median in the Pac 12 distribution, between 50% and 75% of the teams in this conference had eight or more wins. On the other hand, in ACC and Big 10, between 25% and 50% of the teams had eight or more wins, in the SEC exactly 50% of the ...
Read MoreCon USAGood job! Indeed 6 is the median of the Con USA distribution, which tells is that exactly 50% of the teams in this conference had less than six wins. On the other hand, in the ACC, Big 10, and Pac 12 conferences between 25% and 50% of the teams had less than six wins and in the SEC,...
Read MoreIn the previous activity, we compared the distributions of the number of wins of teams in two Division I conferences. When comparing distributions using side-by-side boxplots, you can also compare more than two groups. The following image compares the distributions of the number of football game wins of teams in five Division I conferences in the 2014 season.
X axis is labeled "Football Wins 2014." ACC Boxplot: box spans ~6 to ~9; lower line extends from 3 to ~6; uppline extends from ~9 to ~13. Big 10 Boxplot: box spans 5 to 9.5; lower line extends from 3 to 5; upper line extends from 9.5 to 14. Pac 12 Boxplot: box spans ~5 to 10; lower line extends from 2 to ~5; uppline extends from 10 to ~13. SEC boxplot: box spans 7 to 10; lower line extends from 3 to 7; upper line extends from 10 to 12. Con USA Boxplot: box spans 4 to 8; lower line extends from 3 to 4; upper line extends from 8 to ~13.
For this question consider only the ACC and Big 10. Which of the two conferences had a larger percentage of teams with seven or more wins?
Both conferences had the same percentage of teams with seven or more wins.Good job! Indeed since 7 is the median of both distributions, both conferences had 50% of their teams with seven of more wins....
Read Morehe National Collegiate Athletic Association (NCAA) is divided into three divisions (Division I, II, and III), based roughly on school size. Each division is made up of several conferences for regional league play.
The side-by-side boxplots below compare the distributions of football game wins of teams in two Division I conferences: the Big 10 and SEC (Southeastern Conference) during the 2014 season. (For example, note that the median of the SEC distribution is 8. This means that 50% of the teams in the SEC division had more than eight wins and 50% of the teams had less than eight wins).
X axis is labeled "Football Wins 2014." Big 10 Boxplot: box spans 5 to 9.5; lower line extends from 3 to 5; upper line extends from 9.5 to 14. SEC boxplot: box spans 7 to 10; lower line extends from 3 to 7; upper line extends from 10 to 12.
Based only on the boxplots, which of the two conferences has the most teams?
It is not possible to determine from the information given.Good job! Although boxplots provide a wealth of information about data sets, the number of observations in the data is not something you can determine from a boxplot. You need access to the raw data that is used to create the box plot to det...
Read MoreThe National Collegiate Athletic Association (NCAA) is divided into three divisions (Division I, II, and III), based roughly on school size. Each division is made up of several conferences for regional league play.
The side-by-side boxplots below compare the distributions of football game wins of teams in two Division I conferences: the Big 10 and SEC (Southeastern Conference) during the 2014 season. (For example, note that the median of the SEC distribution is 8. This means that 50% of the teams in the SEC division had more than eight wins and 50% of the teams had less than eight wins).
X axis is labeled "Football Wins 2014." Big 10 Boxplot: box spans 5 to 9.5; lower line extends from 3 to 5; upper line extends from 9.5 to 14. SEC boxplot: box spans 7 to 10; lower line extends from 3 to 7; upper line extends from 10 to 12.
Which conference has a greater percentage of teams with fewer than six wins?
The Big 10Good Job! Indeed, 6 is larger than Q1 (but smaller than the median) in the Big 10 distribution, which tells us that between 25% and 50% of the teams in the Big 10 conference had less than six wins. On the other hand, 6 is less than Q1 of the SEC distribution, which tells us that less than ...
Read More
he following 6 questions relate to the same histogram, shown below.