# Course 3: Statistics for Marketing

## Coursera Study Guide

Click to Enroll in Coursera Meta Marketing Analytics Professional Certificate

## CONTENT

This week you will be introduced to inferential statistics and how to define samples and populations for marketing. You’ll also be introduced to the concept of variables. At the end of the week you will complete part two of your capstone project.

## Learning Objectives

• Identify the value of inferential statistics
• Define sampling and its limitations in the context of marketing (samples & populations)
• Make predictions based on sampling data
• Understand the concept of variables – dependent and independent variables

## PRACTICE QUIZ: SAMPLING

### 1. What is the difference between a population and a sample?

• A population includes every individual in a group, while a sample is a subset of a population used to represent a group. (CORRECT)
• A sample includes every individual in a group, while a population is a subset of a sample used to represent a group.
• These terms are synonymous.
• A population involves people, but a sample does not.

Correct: Good job! A population is a collection of individuals. These individuals can, and often are, actual people, but this is not required. The individuals may be anything. A sample, on the other hand, is a subset of a population used to represent the population it is drawn from.

### 2. Which of the following are conclusions of the Central Limit Theorem?

• I. Large samples should have the same mean and standard deviation as the population.
• II. Large samples normalize data.
• III. The accuracy of data analysis will always increase as more data is collected.
• I and II (CORRECT)
• I and III
• II and III
• All of these are conclusions of the theorem.

Correct: Good job! These are the two main conclusions from the Central Limit Theorem. As the sample size increases, the distribution of the data becomes more like the normal distribution. Moreover, for larger sample sizes the values of some statistics like the mean and standard deviation approach those of the population.

### 3. True or false: The minimum sample size should always be 50% of the population.

• True
• False (CORRECT)

Correct: Good job! In order for your analysis to be accurate, you do need a minimum sample size. Yet, there is no fixed size (relative to the population) that every sample must be. Larger populations can get by with smaller percentage samples, while smaller populations usually require the opposite.

### 4. What does the plateau effect state?

• That larger populations yield more reliable results from analysis.
• That after a certain point, adding more data to the sample will not increase accuracy. (CORRECT)
• That larger sample sizes are always better.
• That all sample sizes are acceptable in performing analysis.

Correct: Good job! Generally, adding more data to your sample is a good way to make your analysis more reliable. At some point, though, when enough points have been included, adding further points will have a negligible effect on the accuracy of your analysis.

### 5. What are the four types of sampling techniques introduced in the lesson?

• I.   Simple random, systematic, stratified, cluster
• II.  Simple random, systematic, fast random, cluster
• III. Simple random, complex random, cluster, point-wise
• I (CORRECT)
• II
• III
• None of these

Correct: Good job! The four types of sampling discussed in the lesson are simple random, systematic, stratified, and cluster. To be sure these are not the only sampling strategies used in data analysis. They are the four most common by a wide margin.

### A company wishes to gauge customer satisfaction. They know that 30% of their population is under the age of 50 and 70% is above the age of 50. They decide to poll 100 customers by choosing 30 customers who are under 50 and 70 who are over 50.

• This is an example of simple random sampling.
• This is an example of stratified sampling. (CORRECT)
• This is an example of systematic sampling.
• This is an example of cluster sampling.

Correct: Good job! Stratified sampling is when the members are chosen for the sample in the same proportion as they appear in the population. Here, choosing 30 individuals under 50 for the sample will give a proportion of 30% in the sample for under 50 individuals. This is the same proportion as the population.

### 7. A company has worksites across the country. Each of the worksites has roughly the same number of employees in similar roles. The company wants to sample their workers, but they are unable to visit all sites to collect their data. How should they go about sampling their population of employees?

• Cluster sampling (CORRECT)
• Simple random sampling
• Systematic sampling
• Stratified sampling

Correct: Good Job! Since each worksite is very similar, the company can pick just some of the sites and sample from those. This is what cluster sampling will do very effectively.

### 8. True or false: When choosing a sample, size doesn’t matter.

• False (CORRECT)
• True

Correct: Good job! In order for your analysis to be accurate, you do need a minimum sample size. Larger populations can get by with smaller percentage samples, while smaller populations often require the opposite.

## PRACTICE QUIZ: DISTRIBUTIONS

### 1. How can knowing the probability distribution of customer data help a marketer?

• I.   It can be used to predict future customer behavior
• II.  It can be used to determine the purchase history of specific customers
• III. It can inform a marketer about customer preferences
• I and II
• I and III (CORRECT)
• II and III
• I, II, and III

Correct: Good job! Knowing the probability distribution of customer data can shed some insight on customer behavior and to predict future customer behavior. Probability distributions cannot be used to determine the purchase history of customers since the purchase history is used to construct the distribution.

### 2. How does data with a high variance affect the shape of a distribution?

• The distribution will have a short, wide shape. (CORRECT)
• The distribution will have a tall, wide shape.
• The distribution will have a short, narrow shape.
•  The distribution will have a narrow, tall shape.

Correct: Good job! Recall that the variance of a dataset indicates how spread out the data is. The more spread out the data is, the wider the distribution will be. Since the area under the curve is fixed based on the sample size, this means that the mean must be shorter as well.

### 3. What does a narrow and tall distribution tell you about the variance of the underlying data?

• That the dataset has low variance. (CORRECT)
• That the variance is increasing
• That the variance is not important.
• That the dataset has high variance.

Correct: Good job! A low variance dataset has data that is not spread out much from the mean. This would show up in the distribution as a narrowing of the graph. Since the area under the curve of a distribution must be equal to the sample size, the peak must be higher so that the area is not diminished.

### 4. Which of the following is not a type of distribution discussed in the lesson?

• I.    Positive
• II.   Exponential
• III.  Poisson
• I (CORRECT)
• II
• III
• All of these

Correct: Good job! Positive is not a distribution at all, much less one that was introduced in the lesson. Exponential and Poisson both were.

### 5. True or false: Data transformations can be used to correct for both skew and kurtosis in the data.

• False (CORRECT)
• True

Correct: Good job! The four transformations discussed in the lesson can be used to correct for skew, but they cannot be used to correct for kurtosis. Correcting for kurtosis may sometimes be accomplished by removing outliers from the dataset.

### 6. What does kurtosis describe?

• It describes how symmetric the data is about the mean.
• It describes how the data may be pulled to the left or the right.
• It describes how wide the data is.
• It describes how data may be pulled up or down relative to the normal distribution. (CORRECT)

Correct: Good job! Positive kurtosis means that the data is pulled upwards when compared to a normal distribution with a peak that tends to be narrower. Negative kurtosis is the opposite, where the peak is flatter and lower than the normal distribution.

### 7. What does skew describe?

• It describes how the data may be pulled to the left or the right. (CORRECT)
• It describes how wide the data is.
• It describes how data may be pulled up or down relative to the normal distribution.
• It describes how sharp the peak of the data is when compared to the normal distribution.

Correct: Good job! Positive skew means that the data has a longer tail to the right (i.e., in the positive direction) while negative skew means that the data has a longer tail to the left.

### Cube Root, Square, Square Root, Logarithmic

• False
• True (CORRECT)

Correct: Good job! These four transformations discussed in the lesson are often useful in removing skew in the data.

## PRACTICE QUIZ: VARIABLE TYPES

### 1. What is a quantitative variable?

• It is a variable that represents only large numbers.
• It is numerical data that is used for labeling.
• It is a variable that represents a numerical value that can be interpreted mathematically. (CORRECT)
• It is a variable that represents numbers that can be counted.

Correct: Nice job! Likely most of the variables that you will see will represent numerical quantities. Moreover, these values can be interpreted and manipulated mathematically.

### 2. Which of the following are examples of quantitative variables?

• I. Sales data
• II. Jacket colors
• III. Ticket prices
• All of these are quantitative data types.
• II and III
• I and III (CORRECT)
• I and II

Correct: Good job! Quantitative data is data comprised of numbers that can be interpreted and manipulated mathematically. Both sales data and ticket prices fall in this category.  Jacket colors, since they are not mathematical, do not qualify.

### 3. Which of the following are examples of qualitative variables?

• I. The amount earned by a charity drive
• II. The order of individuals in a list
• III. Yelp ratings
• I and II
• All of these are qualitative data types.
• II and III (CORRECT)
• I and III

Correct: Good job! Qualitative variables represent numbers that are used as labels or in ranking. Both II and III fall into one of these categories.

### 4. Quantitative variables can be broken down into two categories. What are they?

• Discrete and continuous (CORRECT)
• Discrete and nominal
• Ordinal and continuous
• Nominal and ordinal

Correct: Nice job! Discrete variables are variables that can be counted. Continuous variables, on the other hand, represent measurable quantities that cannot be counted.

### 5. True or false: The position of a company on the Fortune 500 list is an example of an ordinal variable.

• True. (CORRECT)
• False.

Correct: Nice job! An ordinal variable, as the name implies, is a variable with a specific order. These are often found on ranked lists of which the Fortune 500 is one. Even though they often use numbers, these numbers cannot be interpreted mathematically beyond their mathematical order.

### 6. There are two categories of qualitative variables. What are they?

• Nominal and ordinal (CORRECT)
• Ordinal and continuous
• Discrete and continuous
• Discrete and nominal

Correct: Nice job! Both nominal and ordinal are categories of qualitative variables.

### 7. True or false: The number of people in a coffee shop is an example of a continuous variable.

• False. (CORRECT)
• True

Correct: Good job! Continuous variables are uncountable. Clearly, the number of people in a coffee shop can be counted.

### 8. True or false: The color of a ball is an example of a nominal variable.

• True. (CORRECT)
• False

Correct: Nice job! A nominal variable is a variable with no specific order. These are often used as labels even if numbers are involved.

### 9. True or false: The count of cars in a parking lot is an example of a discrete variable.

• True. (CORRECT)
• False

Correct: Good job! Continuous variables are uncountable. Since the count of cars is countable, it is a discrete variable.

## GRADED QUIZ: SAMPLING, DISTRIBUTION, AND VARIABLES

### 1. How does the skew affect the shape of the graph of a distribution?

• Skew determines how narrow the graph is.
• Skew determines how wide the data is.
• Skew determines how tall the graph is.
• Skew will cause the graph to lean either to the left or right. (CORRECT)

Correct: Good job! Positive skew will cause the graph of the distribution to lean to the left and negative skew will cause the graph to lean to the right.

### A university athletics department wants to assess the quality of life for its student athletes. There are 1000 student athletes at the school, with 60% male and 40% female. The department polls 100 athletes, choosing 60 male athletes and 40 female athletes.

• Clustering
• Systematic
• Simple random
• Stratified (CORRECT)

Correct: Good job! To get a representative sample, it is appropriate to maintain the same 60:40 proportion in the sample that exists in the population.

### 3. True or false: Transformations can correct for skew.

• True (CORRECT)
• False

Correct: Good job! There are various transformations that may correct for skew, and four of them were introduced this week.

### 4. What is a quantitative variable?

• A variable that uses numbers as labels.
• A variable that represents numerical rank.
• A variable that represents a quantity. (CORRECT)
• A variable that represents quality.

Correct: Good job! Quantities have numerical, mathematical meaning. Hence the variables that represent them are quantitative variables.

### 5. Which of the following is not an example of a qualitative variable?

• The number of stars on a customer review.
• The place of a runner in a race.
• The square footage of a house. (CORRECT)
• A person’s marital status.

Correct: Good job! As the name suggests, qualitative variables represent qualities of an object. Square footage is a quantity, so it is a quantitative variable.

### 6. Which is a subtype of quantitative variables?

• Discrete (CORRECT)
• Ordinal
• Random
• Nominal

Correct: Good job! Discrete variables are quantities that can be counted.

### 7. What is a qualitative variable?

• A variable that is numeric.
• A variable that represents the size of an object.
• A variable that represents a quantity.
• A variable that represents a quality of an object. (CORRECT)

Correct: Good job! As the name suggests, qualitative variables represent qualities of an object. If numbers are used, they have no mathematical meaning.

### 8. What is the exponential distribution?

• A distribution that gives the probability of something happening based on the number of times something else has happened.
• A distribution that involves a component of time. (CORRECT)
• A distribution that is shaped like a bell.
• A distribution in which all values have an equal chance of happening.

Correct: Good job! Exponential distributions are similar to Poisson distributions, but will involve time.

### A restaurant wants to add a new menu item. The cost of the item to the restaurant is significant, so they only are interested in doing it if they believe that the customers will purchase the dish. They survey the first 20 customers who enter the restaurant each day for a month for feedback.

• Clustering
• Simple random
• Systematic (CORRECT)
• Stratified

Correct: Good job! Systematic sampling occurs when you receive data in a series, or when you select individuals (or groups of individuals) at regular intervals.

### 10. True or false: Transformations cannot correct for kurtosis.

• False
• True (CORRECT)

Correct: Good job! Removing possible outliers may correct for kurtosis, but transformations cannot.

### 11. Which of the following is not an example of a quantitative variable?

• The volume of gasoline in a car’s tank.
• The price of an item on a restaurant menu.
• The time it takes to fly between two cities.
• A person’s phone number. (CORRECT)

Correct: Good job! Variables that use numbers for rank or order are qualitative variables, not quantitative variables.

### 12. What are dependent variables?

• They are variables that are numeric.
• They are the variables that you can control in a test or experiment.
• They are variables that describe the order of objects.
• They are variables that you measure in a test. (CORRECT)

Correct: Good job! Dependent variables depend on the outcome of a test or experiment. Since they are the result of a test, they depend on the test or experiment.

### 13. What is the uniform distribution?

• A distribution that gives the probability of something happening based on the number of times something else has happened.
• A distribution in which all values have an equal chance of happening. (CORRECT)
• A distribution that depends on time.
• A distribution that is shaped like a bell.

Correct: Good job! In a uniform distribution all values have an equal chance of happening because the graph of the distribution is a horizontal line.

### 14. Which of the following is an example of a quantitative variable?

• The amount paid in taxes. (CORRECT)
• A person’s social security number.
• A person’s position in line at the ticket counter.
• The names of the majors at a college.

Correct: Good job! The amount paid in taxes is a numerical value that can be interpreted mathematically. This makes it a quantitative variable.

### 15. Which one of the following is a subtype of qualitative variables?

• Discrete
• Ordinal (CORRECT)
• Continuous
• Random

Correct: Good job! Ordinal variables represent the rank or order of objects. The rank of an object is a quality of that object.

### 16. What is the Poisson distribution?

• A distribution in which all values have an equal chance of happening.
• A distribution that gives the probability of something happening based on the number of times something else has happened. (CORRECT)
• A distribution that depends on time.
• A distribution that is shaped like a bell.

Correct: Good job! Poisson distributions are common when the probability of something happening depends on some other event occurring (or not occurring).

### 17. What are the two subtypes of quantitative variables?

• Discrete and continuous (CORRECT)
• Nominal and discrete
• Continuous and ordinal
• Ordinal and nominal

Correct: Good job! Continuous variables are quantities that can’t be counted. Discrete variables are quantities that can.

### 18. Which of the following is an example of a qualitative variable?

• Your commute time to work.
• Rental prices in your town.
• The days of a month. (CORRECT)
• The number of lions at the zoo.

Correct: Good job! As the name suggests, qualitative variables represent qualities of an object. The days of the months are labels. The one in the first of January does not represent a quantity.

### 19. How does kurtosis affect the shape of the graph of a distribution?

• Kurtosis determines how wide and right-leaning the graph is.
• Kurtosis determines if the graph leans to the right or left.
• Kurtosis determines how short and right-leaning it is.
• Kurtosis will cause the graph to be either tall and narrow or short and wide. (CORRECT)

Correct: Good job! Positive kurtosis will cause the graph of the distribution to be narrow and tall. Negative kurtosis will cause the graph to be short and wide.

### 20. True or false: Transformations can correct for kurtosis.

• True
• False (CORRECT)

Correct: Good job! Removing possible outliers my correct for kurtosis, but transformations cannot.

### 21. A sample is…

• A small subset of a population (CORRECT)
• The majority of a population
• The same thing as a population

Correct: Exactly! A small subset of a population, if chosen with care, can represent an entire population.

### 22. Larger sample sizes…

• Are more likely to have the same mean and standard deviation as the population
• Are more likely to be a normal distribution
• Are important for accurate statistics
• These are all correct (CORRECT)

Correct: Exactly! All of these are true, which makes it important to make sure your sample size is big enough.

### 23. DCB Cleaning mostly works with small or medium companies, but they do also work with a couple large companies.  They want to make sure their survey represents small, medium, and large companies.  What sampling method should they use?

• Stratified Sampling (CORRECT)
• Simple Random Sampling
• Cluster Sampling
• Systematic Sampling

Correct: Exactly! Because DCB Cleaning wants to make sure companies of all sizes are represented, Stratified Sampling is the best choice.

### 24. If your distribution is tall and skinny, what does that tell you about your variance?

• Nothing; there is no connection between variance and distribution.
• The variance is small (CORRECT)
• The variance is high

Correct: Exactly! A tall, skinny distribution tells you that the majority of the data is close to the mean, so the variance is low.

### 25. If Calla and Ivy, a florist, wants to look at how many customers enter the store before they sell one of their big bouquets, what distribution would they expect?

• Normal Distribution
• Uniform distribution
• Poisson Distribution (CORRECT)
• Exponential Distribution

Correct: Exactly! Because you are looking for the probability of one thing happening (selling a big bouquet) based on the count of something else (how many customers enter the store), Poisson would most likely describe your data.

### The above image is an example of what?

• Positive Skew (CORRECT)
• Negative Skew
• Positive Kurtosis
• Negative Kurtosis

Correct: Exactly! The long tail is pointing towards the positive side, so it is a positive skew.

### 27. All numbers are continuous variables.  True or False?

• False (CORRECT)
• True

Correct: Exactly! Some numerical variables are continuous, but they can also be discrete.

### 28. A dog food company wants to record the type of dog a customer owns.  Dog Breed would be what kind of variable?

• Discrete
• Continuous
• Nominal (CORRECT)
• Ordinal

Correct: Exactly! It is a variable that creates groups, but there is no inherent order between them.

### 29. You have two designs for a logo. You create two banner ads, one with each logo, and you count how many times each banner is clicked. In this example, the logo is your…

• Dependent Variable
• Independent Variable (CORRECT)

Correct: Exactly! This is the variable you are controlling that is not influenced by anything else.

### 30. In the context of the graph of a distribution, what is the difference between skew and kurtosis?

• Skew affects the lean of the graph. Kurtosis affects the height and width of the graph. (CORRECT)
• Kurtosis causes the graph to lean to the left. Skew causes the graph to lean to the right.
• Kurtosis affects the lean of the graph. Skew affects the height and width of the graph.
• Kurtosis causes the graph to be short and narrow. Skew causes the graph to be tall and wide.

Correct: Good job! Positive skew will cause the graph of the distribution to lean to the left and negative skew will cause the graph to lean to the right. Positive kurtosis will cause the graph to be narrow and tall, while negative kurtosis will cause the graph to be short and wide.

### A student club at a large high school wants to put on a movie night for the rest of the students. They poll ten students from each class (freshmen, sophomores, etc.) to determine the movie.

• One-at-a-time
• Systematic
• Clustering (CORRECT)
• Simple random

Correct: Good job! The various student classes in a larger school is typically very similar in size.

### 32. What are independent variables?

• They are variables that are numeric.
• They are variables that describe the order of objects.
• They are the variables that you can control in a test or experiment. (CORRECT)
• They are variables that you measure in a test.

Correct: Good job! Because independent variables are can be controlled in tests, they are not influenced by the results of the test — hence, they are independent.

### 33. Which one of the following is a subtype of qualitative variables?

• Nominal (CORRECT)
• Random
• Continuous
• Discrete

Correct: Good job! Nominal variables are used to represent labels. Labels reflect a quality of an object, not a quantity.

### 34. What are the two subtypes of qualitative variables?

• Ordinal and discrete
• Ordinal and nominal (CORRECT)
• Continuous and discrete
• Nominal and continuous

Correct: Good job! Ordinal variables represent the rank or order of objects. Nominal variables represent names or labels of objects. Both of these are qualities of an object.

### 35. What is the difference between independent and dependent variables?

• Dependent variables are quantitative, while independent variables are qualitative.
• Independent variables are quantitative, while dependent variables are qualitative.
• Dependent variables can be controlled in a test or experiment while independent variables are measured.
• Independent variables can be controlled in a test or experiment while dependent variables are measured. (CORRECT)

Correct: Good job! Independent variables do not depend on the results of a test, while dependent variables do.

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