Data Distributions
According to the histogram, what is the most common number of goals scored?
4 goals
What is the statistical variable represented by the following question, and is it categorical or quantitative?
โHow many TV sets are owned by families?โ
The statistical variable is the number of TV sets owned by families. It is quantitative because it asks for an amount, rather than brand or type of TV set.
What is a group of subjects who are not exposed to the variable under study
a control group
What is the name for the type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected.
Simple Random Sampling
Is the following question a statistical question? give a reason for your answer
"How often do you play football?"
It cannot be answered by collecting data. It is only asking about one specific person.
What does it mean for a histogram to be "skewed left"
the data is asymmetrical with a long "tail" extending towards the left side. The majority of data points cluster on the right side of the distribution, and a few lower values pull the tail towards the left.
Diana says she identified a quantitative variable and conducted a survey when she asked her fellow classmates in her homeroom about their favorite style of sweatshirt from the categories: hoodie, pullover, or zip-up. Explain her error.
The survey was conducted on a qualitative, or categorical, variable, rather than a quantitative variable.
A doctor assigns people to treatment groups based on data from their medical records. Is this method of selecting treatment groups biased or unbiased? Give a reason for your answer.
The method is biased because the doctor is using patientsโ medical records to assign them to a group rather than assigning them randomly.
A television news program asks its viewers to call in to give their opinions on an upcoming ballot question. What type of sampling method does this represent?
This represents a self-selected sample.
Use the dot plot to answer the question:
How many bags of m&ms were sampled?
20 bags
Which data distribution is most appropriate to see individual data points?
dot plot
Forty randomly-selected members of a high school music program were asked to report the number of hours they spend practicing each week. If you were to compute the mean number of hours, would your answer be a parameter or a statistic?
The answer is a statistic because the data were collected from a sample, not the entire population.
What type of study is conducted in this scenario:
Linda wanted to know if it is easier for students to memorize a list of common three-letter words than a list of three-letter nonsense words. She randomly selected ๐๐ students in her district. She put ๐๐ blue and ๐๐ red chips in a jar, and without looking, each student chose a chip. Those with red chips were given the list of common words; those with blue chips were given the list of nonsense words. She gave all students one minute to memorize their lists. After the minute, she collected the lists and asked the students to write down all the words that they could remember. She recorded the number of correct words recalled.
Experimental Study
There are five elementary schools in the district.
Susan asked every 5th student going through the lunch line at each school what his or her favorite lunch menu item was.
What sampling method is used in this study? Is the method likely to be biased?
This is systematic sampling. The rule is that every fifth number was chosen. This method unlikely to be biased.
Politician Kevin wants to know the percentage of all adults in the U.S. who said using a cell phone while driving should be illegal. Determine whether the following numerical value is a parameter or a statistic in the given context.
In a recent survey of 416 adults from the U.S., 57% said using a cell phone while driving should be illegal.
statistic
What is the minimum value of the data set?
20
Suppose Hana wants to find out the most commonly driven type of vehicle among the students at her high school. Since 1,560 students attend her high school, she asks every tenth student who enters the building one morning what kind of vehicle he or she drives. What is the population in this scenario?
The population is the 1,560 students that attend Hanaโs high school.
An ice cream shop asks its customers if they would like the shop to offer containers of ice cream to take home. What type of study does this describe?
This study is a sample survey.
What sampling method is used in the following examples? Is the method likely to be biased or not?
The population is grouped according to age and a random sample is chosen from each group.
This is a stratified sample. It is likely to be unbiased.
Which sampling method requires the researcher to divide up the population into subgroups, then select a whole subgroup randomly to form the sample
cluster sampling
For skewed data, which measure of center is most appropriate?
the median
A snack company produces bags of almonds so that each bag contains about the same number of almonds. The bags are filled with an average of 22 almonds. Carter gave each of his friends a bag of almonds for a snack after school. Their 5 bags contained an average of 26 almonds each.
Identify the parameter and the statistic.
The parameter is 22 almonds per bag because that is the average of all of the bags made.
The statistic is 26 almonds per bag because that is the average of the sample of 5 bags.
Determine the type of study described:
A grocery store wonders how many customers bring reusable grocery bags to the store. They have an employee stand at the checkout and count the number of people using reusable bags.
This is an Observational Study, since members of a study are observed and not affected by the study
What sampling method is used in the following examples? Is the method likely to be biased or not?
A number of hospitals around the country were randomly chosen. Within each hospital, all of the nurses were chosen.
This is cluster sampling. Each hospital in the country is a cluster, and some hospitals/clusters were chosen to be a part of the sample. It is unlikely to be biased.
Which measure of center is post appropriate for symmetric data
mean