Distributions/ Shape
Define skewed
A distribution is skewed if the tail on one side of the mode is fatter or longer than on the other: it is asymmetrical.
Define quantitative and categorical data
Quantitative: Has numerical values for which arithmetic operations (e.g., addition or averaging) make sense. Examples: age, height, # of AP classes, SAT score. Categorical: Places an individual into one of several groups or categories. Examples: eye color, race, gender.
What Is used to best describe Parts of an entire hole?
Pie Chart
Q: What should be included in your five number summary?
A: Median, Q1, Q3, min, max
Does skewness affect the mean and or median.
Skewness affects the mean and but not the median.
Is the age range 30-40 categorical or Quantitative
Quantitative, because it represents a measurable quantity.
What does Q2 represent in a box plot?
Median
According to the Census
Bureau, the mean and median 2008 income of people at least 25 years old who had a bachelor’s degree but no higher degree were $48,097 and $60,954. Which of these numbers is the median, and which one is the mean?
Mean: $60,954
Median: $48,097 Graph is skewed right so the mean would be higher
If a distribution is symmetrical, which of the following must be true?
A) The mean must be less than the median
B) The mean is either greater or equal to the median
C) The mean is either less than or equal to the median
D) The median and mean are equal
D) The mean and median are equal
A particularly common question in the study of wildlife behavior involves observing contests between “residents” of a particular area and “intruders.” In each contest, the “residents” either win or lose the encounter (assuming there are no ties). Observers might record several variables. Which of the following variables is categorical? A)the duration of the contest (in seconds) B) the number of animals involved in the contest C)whether the “residents” win or lose D) the total number of contests won by the “residents”
C)whether the “residents” win or lose
In drawing a histogram, which of the following suggestions should be followed?
A)Leave large gaps between bars. This allows room for comments
B)The heights of bars should equal the class frequency
C) Generally, bars should be square so that both the height and width equal the class count
D) The scale of the vertical axis should be that of the variable whose distribution you are displaying
B: The heights of bars should equal the class frequency
A researcher reports that, on average, the participants in his study lost 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report must be a fraud. Which of the following statements is correct?
A)Your friend must not have followed the diet correctly, since she did not lose weight
B)Since your friend did not lose weight, the report must not be correct
C) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results
D) In order for the study to be correct, we must now add your friend's results to those of the study and recompute the new average
C) The report only gives the average. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results
Which of the following is likely to have a mean that is smaller than the median?
A)the salaries of all National Football League players
B)the scores of students (out of 100 points) on a very easy exam in which most score perfectly, but a few do very poorly
C)the prices of homes in a large city
D)the scores of students (out of 100 points) on a very difficult exam on which most score poorly, but a few do very well
D)the scores of students (out of 100 points) on a very difficult exam on which most score poorly, but a few do very well
As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student is a sophomore, a 3 if the student is a junior, and a 4 if the student is a senior. The variable class standing is A) Categorical B) Numerical C) Quantitatively categorical D) all of the above
A) Categorical
The ages of people randomly selected at a playground are 3, 10, 42, 25, 5, 8, 6, 12, 15, 4, 3, 21.
What numbers would you use as your stems to make a stemplot?
0, 1, 2, 3, and 4
Define Standard Deviation.
a measure of how dispersed the data is in relation to the mean
If a distribution is skewed to the right, which of the following is true? (a) The mean must be less than the median. (b) The mean and median must be equal. (c) The mean must be greater than the median. (d) The mean is either equal to or less than the median, (e) It’s impossible to tell which of the above statements is true without seeing the data.
C: The mean is higher greater than the median.
You measure the age, marital status and earned income of an SRS of 1,789 men. The number and type of variables you have measured is…
3 variables
2 quantitative, 1 categorial
Q: Double Jeopardy (points)
Deaths among young people Among persons aged 15 to 24 years in the United States, the leading causes of death and number of deaths in a recent year were as follows: accidents, 15,567; homicide, 5359; suicide, 4139; cancer, 1717; heart disease, 1067; congenital defects, 483. To make a pie chart, you need one additional piece of information. What is it?
A: All of the other deaths besides the ones listed are needed in order to make a pie chart that completes a set of categories from a whole.
Miss Edmond took a sample of scores from a statistic quiz. The five number summary was 0, 7, 9, 10, 10. What % of scores were between 0 and 7?
25%