QUIZ: Chapter 1-4
the area under the curve of a probability distribution
1
For the numbers 10, 12, 16, and 20, the sum of the absolute deviations from 15 is:
14
For the numbers 17, 9, 20, 15, and 11, the number which minimizes the absolute deviations is:
15
For the numbers 3, 6, 9, and 10, the sum of the squared deviations from 8 is: 36
34
For the scores 3, 5, 7, 9, 12, 21, 25, 30, What are the 25th and 80th percentiles based on "Definition 3?"
5.5 and 26
Jane's test scores on her five tests are 90, 87, 70, 97, and 75. Her teacher is going to take the median of the test grades to calculate her final grade. Jane thinks she can argue and get two points back on some of the tests. Which test score(s) should she argue?
87
11. Which of the following are descriptive statistics? a) The mean age of people in Detroit. b) The number of people who watched the super-bowl in the year 2002. c) A prediction of next month's unemployment rate. d) The median price of new homes sold in Miami. e) The height of the tallest woman in the world.
A B D E these four are descriptive statistics. Descriptive statistics are numbers that are used to summarize and describe data. Predicting next month's unemployment rate involves predicting future data, no describing the data at hand. Descriptive statistics are numbers that are used to summarize and describe data. Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand
6. In a box plot, what percent of the scores are between the lower and upper hinges?
Half of the scores are between the upper and lower hinges, or the area represented by the box. The upper hinge represents the 75th percentile and the lower hinge represents the 25th percentile. Therefore, the area between the two represents the 50th percentile, half the results.
5. You have to decide between displaying your data with a histogram or with a stem and leaf display. What factor(s) would affect your choice?
How many data that I have to display is the key factor that would affect my choice. To display a larger amount of data, I would choose a histogram display, because It's more obvious to show the shape of the distribution. For a less amount of data, stem and leaf display is a better choice because it can show the data more specific and contain more information.
which of the following is a random sample of a college student body?
ID numbers that were picked from a table of random numbers
Which of the following are parts of statistics?
Interpretations and decisions based on numbners ang grpahs graphs numerical calculations
10. (True/False) The only way to eliminate uncertainty is to obtain data from a large sample.
It's False, the only way to eliminate uncertainty is to obtain data from the whole population, by receiving a large sample we reduce uncertainty. Uncertainty comes from a margin for error percentage and by having a larger sample size from the existing population we reduce the margin for error in the statistic. Inferential statistics is one of the two main branches of statistics which takes a random sampling of data. Inferential statistics relies on a large sample size to reduce uncertainty in the representation of the population.
Identify the scale of measurement for the following: military title -- Lieutenant, Captain, Major.
Ordinal
15. For the scores 3, 5, 7, 9, 12, 21, 25, 30, calculate the 80th percentile based on "Definition 3."
R = P/100 x (N + 1), since R is not an integer, define IR as the integer portion of R, and define FR as the fractional portion of R. Find the scores with Rank IR and with Rank IR + 1, which means 7th and 8th number, the two numbers are 25and 30. Then interpolate by multiplying the difference between the scores by FR and add the result to the lower score. R = 80/100 x (8 + 1) = 7.2; IR = 7; FR = 0.2; The 80th percentile = 0.2 x (30- 25) + 25 = 26.
9. Categorize the following variables as being qualitative or quantitative, and specify the level of measurement used for each item: Rating of the quality of a movie on a 7-point scale Age Country you were born in Favorite Color Time to respond to a question
Rating of the quality of a movie on a 7-point scale -- quantitative, ordinal (It is ordinal because higher scores are better than lower scores. However, there is no guarantee that the difference between, say, a 2 and a 3 represents the same difference in quality as the difference between a 4 and a 5.) Age -- quantitative, ratio (Age is measured on a ratio scale because, in addition to having the properties of an interval scale, a person's age does, after all, have a meaningful zero point (birth). Since age has a true zero point, it makes sense to say that a 30-year-old is twice as old as a 15-year-old. ) Country you were born in -- qualitative, nominal (The country has no inherent order, thus can only be a nominal scale.) Favorite Color -- qualitative, nominal (The color has no inherent order, thus can only be a nominal scale.) Time to respond to a question -- quantitative, ratio (Although an individual's reaction time is always greater than zero, we conceptualize a zero point in time, and can say that a response of 24 milliseconds is twice as fast as a response time of 48 milliseconds.)
8. If you apply Sturges' rule to a data set including 4000 observations, how many intervals should your histogram have?
Struges rule says- the number of intervals should be closest to = 1+ log2 (N) According to the Struges Rule, 4000 observations would be having 13 intervals as 12 is the closest integer to log2(4096) which is very close to 4000.
Suppose that your data include 4000 observations, and you must choose the number of intervals to represent in your histogram. What does Sturges' rule recommend?
Sturges' rule recommends 13 intervals because this is one more than the base 2 logarithm of 4096 (which is close to the actual number of observations).
14. In a study of the effect of handedness on athletic ability, participants were divided into three groups: right-handed, left-handed, and ambidextrous. Athletic ability was measured on a 12-point scale. Check all that apply. The variable athletic ability is a) discrete. b) qualitative. c) continuous. d) quantitative. e) a dependent variable. f) an independent variable.
The answers are (a) Discrete, (d) Quantitative, (e) A Dependent Variable. First of all, handedness is an independent variable, not athletic ability. Which means that athletic ability is a dependent variable. Since rating scale contains only up to 12 points, therefore, it is not continuous. Furthermore, since athletic ability can be measured and represent numeric values, it is a discrete quantitative variable. As a result, (b) qualitative, (c) continuous, (f) an independent variable are wrong choices.
12. Which of the following is a random sample of a college student body? a) Lisa Meyer, Todd Jones, and Maria Rivera, whose ID numbers were picked from a table of random numbers. b) Every fifth person coming out of the Campus Center between 8:30am and 10:00am. c) All are examples of random samples. d) Every 20th person in the student directory.
The correct answer for number 12 is A because the random sample is pure chance; this specific selection procedure allows for each individual in the population to have an equal chance of getting selected.
2. For the numbers 1, 3, 4, 6, and 12: a) Find the value v for which the mean squared deviation is minimized. b) Find the value v for which the mean absolute deviation is minimized
The median is the value that minimizes the sum of absolute deviations, and the mean is the value that minimizes the sum of the squared deviations. Median = 4 and mean = 26/5 = 5.2.
16. Your younger brother comes home one day after taking a science test. He says that someone at school told him that "60% of the students in the class scored above the median test grade." What is wrong with this statement?
The median was used as a measure of central tendency. the median is the midpoint of a distribution. The median can also be thought of as the 50th percentile. It should use "mean" to replace "median" for correction.
13. Identify the scale of measurement for the following: heat measured in degrees centigrade and a score on a 5-point quiz measuring knowledge of algebra
The scale for heat measured degrees centigrade is intervals because there is no true zero point. Zero degrees does not represent the complete absence of temperature. As for the scale of a 5-point quiz, that would be ordinal because higher scores are better than lower scores indicating that the values are ordered.
1. A sample of 30 distance scores measured in yards has a mean of 7, a variance of 16, and a standard deviation of 4. (a) You want to convert all your distances from yards to feet, so you multiply each score in the sample by 3. What are the new mean, variance, and standard deviation? (b) You then decide that you only want to look at the distance past a certain point. Thus, after multiplying the original scores by 3, you decide to subtract 4 feet from each of the scores. Now what are the new mean, variance, and standard deviation?
a) first given n = 30, mean = 7, variance = 16. However, since all distance from yards to feet by 3, the new mean is 3 * 7 =21, new variance is 9 (3^2) * 16 = 144, new standard deviation is 3 * 4 = 12 b) new mean 4 * 7 = 28 , new variance is 16 (4^2) * 16 = 256, new standard deviation is 4 * 4 = 16 However, I think for the (b), since the mean is affected by the change of origin and scale, the new mean would be (3*7)-4=17 and new variance would be (3^2)*16=144 because variance is affected by the change in origin but not change in scale. Also, the new standard deviation would be still 3*4=12 ( since it is affected by the change in origin).
3. Find the mean and median for the following three variables: A B C A B C 8 4 6 5 4 2 7 6 3 1 3 4 3 4 1
a) mean: 6, median: 6 b) mean: 11/3 or 3.67, median: 4 c) mean: 16/3 or 5.33, median: 6 d) mean: 8/3 or 2.67, median: 3 e) mean: 8/3 or 2.67, median: 3
a qualitative variable is
categorical variable
A stem and leaf display is a good method of displaying large amounts of data
false
Three-dimensional bar charts make it easier to interpret the data.
false
When you have relatively few observations you should use percentages rather than frequencies.
false
which of the following are qualitative variables?
hair color, gender
a symmetric distribution
has no skew
when there are many categories, it is best to use
horizontal bar chart
a random sample is one
in which every sample of a particular size has an equal probability of being selected
positive skew
in which the tail in the positive direction is longer than the tail in the negative direction
two basic divisions of statistics are
inferential and descriptive
Identify the scale of measurement for the following: heat measured in degrees centigrade and a score on a 5-point quiz measuring knowledge of algebra is an example of a(n)
interval and ordinal
Tom's test scores on his six tests are 95, 80, 75, 97, 75, 88. Which measure of central tendency would be the highest?
mean
Identify the scale of measurement for the following categorization of clothing: hat, shirt, shoes, pants
nominal
Uncertainty regarding conclusions about a population can be eliminated if you
obtain data from all members of the populatons
In a study of the effect of handedness on athletic ability, participants were divided into three groups: right-handed, left-handed, and ambidextrous. Athletic ability was measured on a 12-point scale. Check all that apply. The variable athletic ability is
quantitative, dependent variable, discrete
Would the variance of 10, 12, 17, 20, 25, 27, 42, and 45 be larger if the numbers represented a population or a sample?
sample, The variance would be larger if these numbers represented a sample because you would divide by N-1 (instead of just N).
our data come from __________, but we really care most about ____________.
samples; populations
Your teacher decides that he will add 10 points to all of your test grades. Which statistic is not changed by this decision?
standard deviation
When are the mean and the median the same?
symmetric distribution
which of the following are descriptive statistics
the number of people who watched the super-bowl in the year 2002 the median price of new homes sold in Miami the height of the tallest woman in the world the mean age of people in Detroit
The term "bin width" refers to what aspect of a histogram?
the size of each class interval
Which of these is a commonly-used way to define the center of a distribution?
the smallest absolute deviation, the balancing point on a scale, the smallest squared deviation
the frequency distribution contains the frequency of every value in the distribution
true
Higher rates of ice cream consumption and drowning for a city correspond. This leads people to believe that eating ice cream can somehow put you at risk of drowning. Can you think of another interpretation?
yes
You hear in a commercial that 80% of children prefer to eat a certain kind of cereal for breakfast. What do you conclude?
you need to know more about where these data came from before making any decisions