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52 Cards in this Set

  • Front
  • Back

What is a Qualitative Variable?

Qualitative, or categorical, variables allow for classification of individuals based on some attribute or characteristic.


 

What is a Quantitative Variable?

Quantitative variables provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results.

What is a Continuous Variable?

 A continuous variable is a quantitative variable that has an infinite number of possible values that are not countable. A continuous variable may take on every possible value between any two values. 

What is a Discrete Variable?

discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. A discrete variable cannot take on every possible value between any two possible values. 

What is the difference between Observational Studies and Designed Experiments?

An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.  That is, in an observational study the researcher observes the behavior of the individuals without trying to infulence the outcome of the study. If a researcher assigns the individuals in a study to a certain group, intentionally changes the value of an explanatory variable, and then records the value of the response variable for each group, the study is a designed experiment.

What is Simple Random Sampling?

A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occuring.  The sample is then called a simple random sample

What is Stratified Sampling?

stratified sample is obtained by separating the population into nonoverlapping groups called strata and then obtaining a sample from each stratum.  The individuals within each stratum should be homogeneous (or similar) in some way.

What is Cluster Sampling?

cluster sample is obtained by selecting all individuals within a randomly selected collection or group of individuals.

What is Systematic Sampling?

systematic sample is obtained by selecting every kth individual from the population. The first individual selected corresponds to a random number between 1 and k.

What is Convenience sampling?

convenience sample is a sample in which the individuals are easily obtained and not based on randomness. 

Construct a Frequency Distribution Table for Continuous Data (include a class width and class limits).

Explain...

Construct a Frequency Distribution Table for Discrete Data (include a class width and class limits).

Explain...

Draw a Histogram, including chart title, axis labels and correct scaling.

Explain...

Construct and describe (how to read) a Stem-and-leaf Plot.

Explain...

Describe a Bell-shaped distribution.

In a bell-shaped distribution the highest frequency occurs in the middle and the frequencies tail off to the right and left of the middle. 

Describe a Skewed-left distribution.

A distribution is skewed-left when the tail to the left of the peak is longer than the tail to the right of the peak. 

Describe a Skewed-right distribution.

A distribution is skewed-right when the tail to the right of the peak is longer than the tail to the left of the peak.

Describe a Uniform distribution.

A distribution is uniform in the frequency of each value when each value of the variable is evenly spread out across the values of the variable.

Describe how Skewed distributions and Outliers affect the mean and median.

Outliers pull the mean away from the median because the mean is sensitive to outliers, but the median is resistant to outliers. The direction of skewedness refers to the side (of the median) the outliers are on, or the side with the longer tail. So when a distribution is skewed right the mean is greater than the median and when a distribution is skewed left the mean is less than the median.


 

What's the difference between Parameter and Statistic?

statistic is a numerical summary of a sample, whereas a parameter is a numerical summary of a population.

What is the Mean?

The mean of a variable is computed by adding all the values of the variable in the dataset and dividing by the number of observations. The population mean (symbol "µ") is computed using all the individuals in a population (parameter). The sample mean (symbol "x-bar") is computed using sample data (statistic).

What is the Median?

The median of a variable is the value that lies in the middle of the data when arranged in ascending order.  We use "M" to represent the median.  


 


Step 1) Arrange the data in ascending order


Step 2) Determine the number of observations, n.


Step 3) Determine the observation in the middle of the data set.


 


(If the number of observations is odd, then the median is the data value exactly in the middle of the data set.  That is, the median is the observation that lies in the [n+1]/2 position.


 


If the number of observations is even, then the median is the mean of the two middle observations in the data set.  That is, the median is the mean of the observations that lie in the [n/2] position and the [n/2 + 1] position.

What is the Mode?

The mode of a variable is the most frequent observation of the variable that occurs in the dataset.


 


Note: A set of data can have no mode, one mode, or more than one mode. If no observation occurs more than once we say the data have no mode.

What is the Range of a Population?  Of a Sample?

The rangeR, of a variable is the difference between the largest and the smallest data value. That is, range = R = largest data value - smallest data value.

What is the Variance of a Population?  Of a Sample?

The variance of a variable is the square of the standard deviation. The population variance is [σ²] and the sample variance is [s²]. 

What is the Standard Deviation of a Population?  

The population standard deviation of a variable is the square troot of the sum of squared deviations about the population mean divided by the number of observations in the population, N.  That is, it is the square root of the mean of the square...

The population standard deviation of a variable is the square troot of the sum of squared deviations about the population mean divided by the number of observations in the population, N.  That is, it is the square root of the mean of the squared deviations about the population mean.


The population standard deviation is symbolically represented by σ (lowercase sigma).


Where µ is the population mean. 

What is the Empirical Rule?

If a distribution is roughly bell-shaped, then

 

approximately 68% of the data will lie within 1 standard deviation of the mean.

 

approximately 95% of the data will lie within 2 standard deviations of the mean.

 

approximately 99.7% of t...

If a distribution is roughly bell-shaped, then


 


approximately 68% of the data will lie within 1 standard deviation of the mean.


 


approximately 95% of the data will lie within 2 standard deviations of the mean.


 


approximately 99.7% of the data will lie within 3 standard deviations of the mean.


 


Note: we can also use the Empirical rule based on sample data.

What is the Chebyshev's Theorem (Chebyshev's Inequality)?

How do you compute Z-Scores?

The z-score represents the distance that a data value is from the mean in terms of the number of standard deviations.  We find it by subtracting the mean from the data value and dividing this result by the standard deviation. There is both a popu...

The z-score represents the distance that a data value is from the mean in terms of the number of standard deviations.  We find it by subtracting the mean from the data value and dividing this result by the standard deviation. There is both a population z-score and a sample z-score.


 

How do you use Z-Scores to compare data from two different populations (as in example 1 in section 3.4)?

Compute the z-score for both populations. The population with the higher z-score had the better outcome.

How do you find a Percentile and Percentile Rank?

The kth percentile, denoted P sub k, of a set of data is a value such that k percent of the observations are less than or equal to the value.

The kth percentile, denoted P sub k, of a set of data is a value such that k percent of the observations are less than or equal to the value.

How do you find a Quartile?

Quartiles divide data sets into fourths, or four equal parts. The first quartile, denoted Q sub 1 divides the bottom 25% of the data from the top 75%.  Therefore, the first quartile is equivalent to the 25th percentile. The second quartile, Q su...

Quartiles divide data sets into fourths, or four equal parts. The first quartile, denoted Q sub 1 divides the bottom 25% of the data from the top 75%.  Therefore, the first quartile is equivalent to the 25th percentile. The second quartile, Q sub 2, divides the bottom 50% of the data from the top 50%; it is equivalent to the 50th percentile or the median. Finally, the third quartile, Q sub 3, divides the bottom 75% of the data from the top 25%; it is equivalent to the 75th percentile.

What is the relationship between OutliersSkewness, and Mean and Median?

Outliers "pull" the mean away from the median, because the mean is sensitive to outliers, but the median is resistant to outliers.  The direction of skewness refers to the side the outliers are on or the side with the longer tail.

What is a 5-Number Summary?

The 5-number summary of a set of data consists of the smallest data value, Q sub 1, the median, Q sub 3, and the largest data value. We organize, the 5-number summary as follows: 

 

 

The 5-number summary of a set of data consists of the smallest data value, Q sub 1, the median, Q sub 3, and the largest data value. We organize, the 5-number summary as follows: 



What is IQR?

The Interquartile range, IQR, is the range of the middle 50% of the observations in a data set.  That is, the IQR is the difference between the third and first quartiles and is found using the formula


 


IQR = Q3 - Q1

What are Outliers?

When performing any type of data analysis, we should always check for extreme observations in the data set.  Extreme observations are referred to as outliers.  


 


Note: outliers do not always occur because of errors. Sometimes extreme observations are common within a population. 

What are Box-and-Whisker Plots?

What is the general Addition Rule for probabilities?

The sum of all probabilities must equal 1 exactly. (That is, 100%)

In probabilities, what are Independent Events?

Independent Events are not affected by previous events. 


A coin does not "know" it came up heads before ...each toss of a coin is a perfect isolated thing.


 


Example: You toss a coin and it comes up "Heads" three times ... what is the chance that the next toss will also be a "Head"?


The chance is simply ½ (or 0.5) just like ANY toss of the coin.


What it did in the past will not affect the current toss!

In probabilities, what are Complement Events?

Complement of an Event

Let S denote the sample space of a probability experiment and let E denote an event. The complement of E, denoted E^c, is all outcomes in the sample space S that are not outcomes in the event E.  Because E and E^c are mu...

Complement of an Event


Let S denote the sample space of a probability experiment and let E denote an event. The complement of E, denoted E^c, is all outcomes in the sample space S that are not outcomes in the event E.  Because E and E^c are mutually exculsive.


 


P(E or E^c) = P(E) + P(E^c) = P(S) = 1


 


Subtracting P(E) from both sides, we obtain the following results:



What does Disjoint/Mutually Exclusive events mean?

Two events are disjoint if they have no outcomes in common.  Another name for disjoint events is mutually exclusive events.


 


Hint: Think ven diagrams where the circles don't intersect.

What does Independent mean?

Two events E and F are independent if the occurence of event E in a probability experiment does not affect the probability of event F.

What does Dependent mean?

Two events are dependent if the occurence of event E in a probability experimet affects the probability of event F.

What are Conditional Probabilities and how are they notated?

Conditional Probability


 


The notation P(F|E) is read "the probability of event F given event E."  It is the probability that the event F occurs, given that the event E has occured.

What is a Descrete Probability Distribution (DPDs)?

The probability distribution of a discrete random variable X provides the possible values of the random variable and their corresponding probabilities.  A probability distribution can be in the form of a table, graph, or mathematical formula. 

 

The probability distribution of a discrete random variable X provides the possible values of the random variable and their corresponding probabilities.  A probability distribution can be in the form of a table, graph, or mathematical formula. 


 

How do you find the Mean or Expected Value of a DPD (particularly for lotteries or games like roulette)?

Describe a Binomial Probability Distribution (BPDs)?

How do you find the Mean of a BPD?

How do you find the Standard Deviation of a BPD?

How deos p (probability of success) and sample size n affect shape (skewness and spread) of the binomial distribution?

What is an Unusual Event?

An event is unusual when p (probability of success) is less than 5% (p < 5%).

What is the Standard Deviation of a Sample?

The sample standard deviation, s, of a variable is the square root of the sum of squared deviations about the sample mean divided by n - 1, where n is the sample size.

 

The sample standard deviation, s, of a variable is the square root of the sum of squared deviations about the sample mean divided by n - 1, where n is the sample size.