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Terms in this set (60)
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 __
categorical
A survey records many variables of interest to the researchers conducting the survey. Which of the following variables, from a survey conducted by the U.S. Postal Service, is categorical?
county of residence
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?
whether the "residents" win or lose
A description of different houses on the market includes the following three variables. Which of these variables is quantitative?
the square footage of the house,
the monthly gas bill,
the monthly electric bill
A professor records the values of several variables for each student in her class. Which of the following variables is categorical?
final grade for the course (A, B, C, D, or F)
When drawing a histogram it is important to
label the vertical axis, so the reader can determine the counts or percent in each class interval.
In drawing a histogram, which of the following suggestions should be followed?
The heights of bars should equal the class frequency.
What percent of the schools have an acceptance rate of less than 20%?
16%
Which interval contains fewer than half of all the observations?
30% - acceptance rate < 45%
The percentage of students with under $10 in their possession is closest to
50%.
The histogram
is skewed to the right,
has an outlier,
is asymmetric.
The number of students with over $30 in their possession is
about 10.
The percentage of these winning jumps that were at least 7 feet (84 inches) is about
37%.
This stemplot is most similar to
a histogram with class intervals 110<score<120, 120<score<130, ect
To which of the following data sets does the stemplot correspond?
D
Below is a bar graph of class standing for a seminar containing seven students who are either freshman, sophomores, juniors, or seniors. The number of students in the seminar who are juniors
is 3.
Based on this pie chart, we may conclude that
more than half of the cars in the study were from the United States.
The number of burglaries in December 1989, the last date recorded in the timeplot, was about
22.
The maximum number of burglaries for a month in 1988 was about
35.
How do you display categorical variables?
bar graphs and pie charts
How do you display quantitative variables?
dotplots, stemplot, histogram, ogive, and timeplot
mean
not a resistant measure of a center
median
resistant measure of a center
to find an outlier
IQR=Q3-Q1.
smaller than = Q1-(1.5xIQR)
larger than = Q3+(1.5xIQR)
Five-number summary
Minimum Q1 Median Q3 Maximum
modified boxplot
outliers plotted individually
Properties of the Standard Deviation
1) s measures spread about the mean and should only be used when the mean is chosen as the measure of center
2) s=0 only when there is no spread. This happens only when all observations have the same value. Otherwise, s>0. As the observations become more spread out about their mean, s get larger.
3) s, like the mean, is not resistant. Strong skewness or a few outliers can make s very large
effects of linear transformation
1) multiplying each observation by a positive number b multiples both measures of center (mean and median) and measures of spread (standard deviation and IQR) by b
2) adding the sam number a (either positive or negative ) to each observation adds a to measures of center and to quartiles, but does not change measures of spread
A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered. Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The mean salary for the employees will
increase by $3000
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?
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.
What is true about the median age?
It must be 20.
The mean age of five people in a room is 30 years. One of the people, whose age is 50 years, leaves the room. The mean age of the remaining four people in the room
is 25.
The median salary of the 20 employees is
$48,000.
Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The median salary for the employees working for the company will
increase by $3000.
The median age of five people in a room is 30. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room
cannot be determined from the information given.
A set of data has a median that is much larger than the mean. Which of the following statements is most consistent with this information?
A stemplot of the data is skewed left.
In a class of 100 students, the grades on a statistics test are summarized in the following frequency table.
71-80.
A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data is ordered. The first quartile of the 20 salaries is
$39,000
The interquartile range of the 20 salaries is
$21,500
Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The interquartile range of the salaries for the employees will
be unchanged.
The five-number summary of a set of data is
the minimum, first quartile, median, third quartile, and maximum.
In a statistics class with 136 students, the professor records how much money each student has in his or her procession during the first class of the semester. The histogram below is of the data collected. From the histogram, which of the following is true?
The mean is much larger than the median.
This is a standard deviation contest. Which of the following sets of four numbers has the largest possible standard deviation?
0, 0, 10, 10
The rental values (in dollars) of a sample of four available apartments close to the university are 470, 600, 580, 550. The standard deviation of the sample is
$57.15
The standard deviation of 16 measurements of people's wights (in pounds) is computed to be 5.4. The variance of these measurements is
29.16
Based on this boxplot, which of the following statements is true?
The interquartile range is about $20,000.
Based on this boxplot, which of the following statements is true?
The salary distributions is fairly symmetric,
About 10 employees make more than $50,000,
Nobody makes more than $80,000.
Based on this boxplot, the five-number summary is
28, 39, 48, 60.5, 77.
Empirical rule
68-95-99.7
A density curve is a curve that
1) is always on or above the horizontal axis
2) has an area exactly 1 underneath it
Normal curves are
symmetric,
single-peaked,
and belled-shaped.
Normal distributions are important in statistics because
1) Normal distributions are good descriptions for some distributions of real data.
2) Normal distributions are good approximations to the results of many kinds of chance outcomes.
3) Many statistical inference procedures based on normal distributions work well for other roughly symmetric distributions.
For this density curve, which of the following is true?
It is symmetric,
The total area under the curve is 1,
The median is 1.
For this density curve, what percentage of the observations lies above 1.5?
25%
For this density curve shown what percentage of the observations lies between 0.5 and 1.2?
35%
For this density curve displayed below. the mean is
0.5.
The normal density curve has which of the following properties?
It is symmetric,
It has a peak centered above its mean,
the spread of the curve is proportional to the standard deviation
Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a normal distribution with mean 90 grams and a standard deviation of 1 gram. Using the 68-95-99.7 rule, what percentage of the items will either weigh less than 87 grams or more than 93 grams?
0.3%
For the density curve below, which of the following is true?
The mean is less than the median.
The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68-95-99.7 rule, what percentage of students will complete the exam in under an hour?
16%
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