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Populations and Samples Solutions

• Statistics is the art and science of:
  •    formulating statistical questions   
  •    collecting data   
  •    analyzing data   
  •    interpreting the results   
• The study of statistics has its own    vocabulary    .

Descriptive Statistics

• Descriptive statistics summarize a population through    charts, graphs, and tables    . (i.e., Measures of center can be used to describe the entire group.)
• In descriptive statistics, you can only describe    the information available to you    .

• Common phrases include:
  •    calculate the measures of   
  •    how many   
  •    what is the average   

Descriptive Statistics Vocabulary

• A    population    is the entire group (every single person, thing, etc.) from which the data is gathered.
• A    census    is a survey or study that collects data from every individual in the population.
• A    parameter    is a characteristic or measure that describes the entire population. Parameters are determined from a census.

Note

Conducting a census is often unrealistic because the population can be extremely large, and getting the entire population to participate is impractical.

•    Data values    (or elements, or individuals) are the people or things that make up the population. A collection of individual data values is called a    data set    .

Inferential Statistics

• Inferential statistics    generalize or infer from a sample    what will likely happen within the population.
• In inferential statistics, probability is used to determine    the chance of occurrence    (or make a reasonable guess) for the population based on the sample.
• Common phrases include:
  •    make a prediction   
  •    draw a conclusion   
  •    cause a change   
  •    describe the relationship between   

Inferential Statistics Vocabulary

• A    sample    is a subset (or part) of a population from which data is collected.
  • Most often, samples are analyzed to draw conclusions (make inferences) about the population because conducting a census is not practical.

• A    sample statistic    , or statistic, is a calculation that is determined by using the data from the sample.
  • It is most often simply called a statistic because it is understood    that an entire population    is rarely used.
  • Statistical estimates about the population are made using    proportions or percentages    .
  • The population’s response is estimated using statistics that include    a margin of error    .

Example 1

Identify the population and sample from the scenario. 

Example 2

Determine if the question will result in descriptive or inferential statistics. Then name the population.

1. What is the $$\begin{gathered} \mathrm{average} \\ \mathrm{descriptive} \end{gathered}$$ miles per gallon for $$\begin{gathered} \text{all trucks manufactured in 2019}? \\ \mathrm{population} \end{gathered}$$

2. Are the  $$\begin{gathered} \mathrm{variations} \\ \mathrm{inferential} \end{gathered}$$ in $$\begin{gathered} \text{class test scores} \\ \mathrm{population} \end{gathered}$$   $\text{statistically significant}?$

3. Has the new attendance policy $$\begin{gathered} \text{impacted} \\ \mathrm{inferential} \end{gathered}$$ $\text{student}$ attendance at $$\begin{gathered} \text{VHS}? \\ \mathrm{population} \end{gathered}$$