STAT Exam 1

mean

- average

IQR formula

Q3-Q1

Which measure of​ spread, the​ range, IQR, or standard​ deviation, is least affected by the​ outlier? Why? A. The IQR is least affected because it does not take the magnitudes of extreme values into account. B. All the measures of spread are affected by the outlier equally. C. The standard deviation is least affected because its value changed the least. D. The range is least affected because its value changed the least.

The IQR is least affected because it does not take the magnitudes of extreme values into account.

chose and example of each a discrete variable and a concrete variable Give an example of each type. A. The distance between two cities is a discrete​ variable, while the number of pets in a household is a continuous variable. B. The number of children in a family is a discrete​ variable, while the time it takes to run a marathon is a continuous variable. C. The number of copies of a video game sold is a discrete​ variable, while the number of cows on a farm is a continuous variable. D. The weight of an animal is a discrete​ variable, while the height of a giraffe is a continuous variable.

The number of children in a family is a discrete​ variable, while the time it takes to run a marathon is a continuous variable.

median

middle

mode

most

This type of bar​ chart, with categories listed in order of​ frequency, has a special name. What is​ it? a. Pie chart b. Dot plot c. Histogram d. Stem-and-leaf e. Pareto

pareto

true or false sample survey is an example of an observational study

true; a sample survey is an example of an observational study

conditional probability & formula

-P(B|A) = P(A and B) / P(A) * read as the probability of B given A - the probability that the event will occur given the knowledge that event A has already occured

A couple plans to have four children. The father notes that the sample space for the number of girls the couple can have is​ 0, 1,​ 2, 3, and 4. He goes on to say that since there are five outcomes in the sample​ space, and since each child is equally likely to be a boy or​ girl, all five outcomes must be equally likely.​ Therefore, the probability of all four children being girls is​ 1/5. Explain the flaw in his reasoning. A. The outcomes are not equally likely. B. The sample space has less than 5 possible outcomes. C. The argument is only correct if each child is equally likely to be a boy or girl. D. The sample space has more than 5 possible outcomes.

. The outcomes are not equally likely.

Give an example of a quantitative variable. Select all that apply. A. Sex B.Age. C.Amount of precipitation D. Education level

- age - amount of precipitation

sample survery

- does not apply a treatment - ex: of an observational survery

what does a zero in standard deviation indicate

a zero indicates no variability in the data set

give an example of a categorcal variable a. dating status b. GPA c. gender d. height

- dating status - gender

determining the fences

- lower fence = Q1- 1.5 (IQR) - upper fence = Q3 + 1.5(IQR)

What is an advantage of the standard deviation over the​ IQR? A. The standard deviation uses all the​ data, while the IQR uses all the data except outliers. B. The IQR is an​ average, while the standard deviation is the actual value. C. The standard deviation takes into account the values of all​ observations, while the IQR only uses some of the data. D. The IQR is more difficult to​ determine, while the standard deviation can be found easily.

The standard deviation takes into account the values of all​ observations, while the IQR only uses some of the data.

. Is the variable continuous or​ discrete? Why? A. The number of people at a concert B. the length of a newborn baby C. The length of time to run a marathon D. the characters typed per minute

a. The number of people at a concert is a discrete variable since it has a finite number of possible values. b. the length of a newborn baby is a continuous variable since it has an infinite continuum of possible values. c. the length of time to run a marathon is a continuous variable since it has an infinite continuum of possible value d. the characters typed per minute is a discrete variable since it has a finite number of possible values.

eighty people with sore legs are randomly divided into two groups. one group is treated weekly with laughing sessions and excercise. the other is treated without laughing sessions what is the response and explantantory variable is the study observational or experimental

response: level of leg soreness explanatory: whether or not the person participated in laughing sessions - study is an experiment because the researchers assign subjects to certain experimental conditions and observe the outcomes of the response variables

Is the variable categorical or​ quantitative? Why? A. Size of home is a categorical variable. Its values are not numerical. B. Size of home is a categorical variable. Its values are numerical. C. Size of home is a quantitative variable. Its values are not numerical. D. Size of home is a quantitative variable. Its values are numerical.

size of home is a quantitative variable. its values are numerical

Explain the difference between a discrete variable and a continuous variable. Choose the correct answer below. A. A discrete variable has infinitely many possible​ values, while a continuous variable is usually a count. B. A discrete variable has each observation belong to one of a set of distinct​ categories, while a continuous variable has observations that take numerical values that represent different magnitudes of the variable. C. A discrete variable has observed values that are clustered in certain​ intervals, while a continuous variable has observed values that are evenly distributed throughout the distribution. D. A discrete variable has possible values that are separate​ numbers, while a continuous variable has possible values that form an interval.

A discrete variable has possible values that are separate​ numbers, while a continuous variable has possible values that form an interval.

What is the advantage of using a graph to summarize the results instead of merely stating the percentages for each​ source? A. A graph allows the viewer to easily see the center of the distribution. B. A graph allows the viewer to associate a shape with each category. C. A graph allows the viewer to more easily judge the relative sizes of the percentages in each category. D. A graph gives the viewer a better sense of the data because it associates a number with each category.

A graph allows the viewer to more easily judge the relative sizes of the percentages in each category.

. What is the difference between categorical and quantitative​ variables? A. A variable is called categorical if each observation is measured numerically. A variable is called quantitative if observations on it represent different magnitudes of the variable. B. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it can be placed into one singular categorical group. C. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. D.A categorical variable is any characteristic observed in a study. A quantitative variable is the numerical value associated with each characteristic.

A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable.

a. Choose the reason why the mean is not the simple average of the possible values. A. The mean should be computed by averaging the​ probabilities, not the possible values. B. The possible value of 0 skews the mean when computed in this fashion. C. The probabilities of each possible value are not all the same. D. There are not enough possible values of x to compute the mean.

The probabilities of each possible value are not all the same.

Why is the standard deviation usually preferred over the​ range? A. The range is an​ average, while the standard deviation is the actual value. B. The range only uses the largest and smallest​ observations, while the standard deviation uses all the data except the outliers. C. The range is more affected by an​ outlier, and the standard deviation uses all the data. D. The standard deviation is sometimes​ negative, while the range never is.

The range is more affected by an​ outlier, and the standard deviation uses all the data.

Choose the correct interpretation of the standard deviation below. A. The standard deviation represents finding the deviation for each​ observation, squaring each​ deviation, and then adding them up. B. Since the standard deviation uses the square of the units of measurement for the original​ data, it is not easy to interpret. C. The standard deviation represents a typical distance of an observation from the mean. D. The standard deviation represents the sum of the deviations from the mean.

The standard deviation represents a typical distance of an observation from the mean.

Is the variable categorical or​ quantitative? Why? A Favorite color is a quantitative variable. Its values are not numerical. B. Favorite color is a categorical variable. Its values are numerical. C.Favorite color is a quantitative variable. Its values are numerical. D. Favorite color is a categorical variable. Its values are not numerical

favorite color is a categorical variable. its values are not numerical

Is the variable categorical or​ quantitative? Why? A.Beverage preference is a categorical variable. Its values are not numerical. B.Beverage preference is a quantitative variable. Its values are numerical. C. Beverage preference is a quantitative variable. Its values are not numerical. D.Beverage preference is a categorical variable. Its values are numerical.

beverage preference is a categorical variable. its values are not numerical

true or false a negative value possible using standard deviation

false; a negative value is impossible using standard deviation

give an example of a quantitative variable a. age b. education level c. sex d. amount of precipitation

- age - amount of precipitation

Which of these values are used in the box​ plot? Select all that apply. a. maximum B. minimum C. median D. Q3 E. Q1 . F.mean G.standard deviation

- maximum - minimum - median - Q1 - Q3

obersvational study vs experiement

- observational study: draws data from a sample to a population where the variable is not under the control of the researcher ; does not apply a treatement to survery respondenets ; only observes survey responses - experiment: a test under controlled conditions that is made to demonstrate a known truth, to examine the validity of a hypothesis, or to determine the efficacy of something previously untried

Give an example of a categorcal variable. Select all that apply. A. Type of residence B. Height C. Gender D. GPA

- type of residence - gender

Why is the IQR sometimes preferred to the standard​ deviation? A. The IQR only includes the largest and smallest​ observations, so it is easier to calculate. B. The IQR only uses a quarter of the​ data, while the standard deviation uses all the data. C. The IQR is not affected by an​ outlier, while the standard deviation is affected by an outlier. D. The IQR uses all the data except the​ outliers, while the standard deviation uses all the data.

The IQR is not affected by an​ outlier, while the standard deviation is affected by an outlier. Your answer is correct.

Which is easier to sketch relatively​ accurately, a pie chart or a bar​ chart? A. A pie chart is easier because estimating the size of the slices in a pie chart is easier than estimating the heights of the bars in a bar graph. B. A bar chart is easier because sketching the exact percentages is more challenging in a pie chart. C. A bar chart is easier because the bars are always in decreasing order of category percentages which makes comparisons of categories easier. D. A pie chart is easier because a pie chart has one shape​ (a circle) which is easier to graph more accurately than a bar graph which has multiple shapes​ (multiple rectangles).

A bar chart is easier because sketching the exact percentages is more challenging in a pie chart.

Explain the difference between a discrete variable and a continuous variable. Choose the correct answer below. A. A discrete variable has each observation belong to one of a set of distinct​ categories, while a continuous variable has observations that take numerical values that represent different magnitudes of the variable. B. A discrete variable has infinitely many possible​ values, while a continuous variable is usually a count. C. A discrete variable has observed values that are clustered in certain​ intervals, while a continuous variable has observed values that are evenly distributed throughout the distribution. D. A discrete variable has possible values that are separate​ numbers, while a continuous variable has possible values that form an interval.

A discrete variable has possible values that are separate​ numbers, while a continuous variable has possible values that form an interval.

a. What is the difference between categorical and quantitative​ variables? A.. A variable is called categorical if each observation is measured numerically. A variable is called quantitative if observations on it represent different magnitudes of the variable. B. A categorical variable is any characteristic observed in a study. A quantitative variable is the numerical value associated with each characteristic. C. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it can be placed into one singular categorical group. D. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable.

A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable.

What is the effect of the​ outlier? A. Range increases and standard deviation decreases when an outlier is added. B. Range decreases and standard deviation increases when an outlier is added. C. Both the range and standard deviation decrease when an outlier is added. D. Both the range and standard deviation increase when an outlier is added.

Both the range and standard deviation increase when an outlier is added.

The workers and the management of a company are having a labor dispute. Explain why the workers might use the median income of all the employees to justify a raise but management might use the mean income to argue that a raise is not needed. Choose the correct answer below. A. Management would want to use the mean because the mean would be higher due to the outliers. The workers would prefer the median because it is not affected by the outliers and would be smaller. B. Management would want to use the mean because the mean would be higher and it is not affected by the outliers. The workers would prefer the median because it is not affected by the outliers and would be larger. C. Management would want to use the mean because the mean would be lower due to the outliers. The workers would prefer the median because it is affected by the outliers and would be larger. D. Management would want to use the mean because the mean would be lower and it is not affected by the outliers. The workers would prefer the median because it is affected by the outliers and would be smaller.

Management would want to use the mean because the mean would be higher due to the outliers. The workers would prefer the median because it is not affected by the outliers and would be smaller.

What is the relevance of the​ IQR? A. The IQR summarizes the range within one standard deviation of the mean. B. The IQR summarizes the range for the lower half of the data. C. The IQR summarizes the range for the upper half of the data. D. The IQR summarizes the range for the middle half of the data.

The IQR summarizes the range for the middle half of the data.

Given an example of each type. Choose the correct answer below. A. The number of copies of a video game sold is a discrete​ variable, while the number of cows on a farm is a continuous variable. B. The weight of an animal is a discrete​ variable, while the height of a giraffe is a continuous variable. C. The number of children in a family is a discrete​ variable, while the time it takes to run a marathon is a continuous variable. D. The distance between two cities is a discrete​ variable, while the number of pets in a household is a continuous variable.

The number of children in a family is a discrete​ variable, while the time it takes to run a marathon is a continuous variable.