Questions and Answers
What percentage of the 1000 registered voters belonged to one of the traditional two parties (Democratic and Republican)?
75%
Who got the fewest votes in the student council presidential election?
Ann
What are the categories by which data are grouped?
Classes
The _____ class limit is the smallest value within the class and the _____ class limit is the largest value within the class.
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What is the difference between consecutive lower class limits called?
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The shape of the distribution shown is best classified as skewed left.
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Which chart is best for presenting the heights of 1,500 students?
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Histograms are used for numerical data while bar charts are suitable for categorical data.
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Explain how the graph about robberies in the afternoon hours is misleading.
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How is the graph misleading regarding financials?
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What type of graphic illustrates the ideal family size based on a survey?
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Why is the chart displaying average consumer's Valentine's Day spending inappropriate? (Select all that apply)
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Which graph does a good job revealing the average per kilowatt-hour prices of electricity?
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What does a correlation coefficient of 0.12 indicate?
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What is the IQR (Interquartile Range) in the context of descriptive statistics?
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What effect will an influential observation have upon the graph of the least squares regression line?
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What can be concluded about a student's score in the 78th percentile?
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What is statistics?
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A(n) _________ is a person or object that is a member of the population being studied.
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1__________ statistics consists of organizing and summarizing information collected, while 2__________ statistics uses methods that generalize results obtained from a sample to the population.
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What is a numerical summary of a sample?
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What is a numerical summary of a population?
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_________ are the characteristics of the individuals of the population being studied.
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Is the quarterback's completed percentage a parameter or a statistic?
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Is the favorite musical band variable qualitative or quantitative?
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Is the rock group variable qualitative or quantitative?
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Is the favorite musical style variable qualitative or quantitative?
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Is the street name of address variable qualitative or quantitative?
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Is the amount of fabric needed for a dress variable discrete or continuous?
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Is the number of touchdowns thrown by a quarterback variable discrete or continuous?
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What is a polling organization’s population in a study of teenagers attending concerts?
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What is the difference between an observational study and a designed experiment?
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What is confounding in a study?
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The study of professional musicians’ ages is an experiment.
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What type of sampling is utilized when Toyota surveys customers?
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What type of bias is indicated when individuals volunteer for a survey?
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The variable measured in an experiment is called _______.
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_______ is a condition applied to the experimental units involved in an experiment.
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An experiment in which neither the experimental unit nor the researcher knows the treatment is called a _______.
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What is the treatment in the soybean yield experiment?
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The goal of an experiment is to determine the effect of treatment on the response variable.
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What does it mean when sampling is done without replacement?
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What type of sampling is used when a newspaper asks readers for their opinions?
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What is an outlier in a dataset?
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Study Notes
Statistics Overview
- Statistics involves collecting, organizing, summarizing, and analyzing data to draw conclusions and provide confidence in results.
- The distinction between descriptive and inferential statistics:
- Descriptive statistics summarize and organize data.
- Inferential statistics generalize findings from a sample to a larger population while assessing reliability.
Key Terms
- Individual: A member of the population being studied.
- Statistic: Numerical summary of a sample.
- Parameter: Numerical summary of a population.
- Variables: Characteristics observed in individuals from a population.
Types of Variables
- Qualitative Variables: Describe attributes (e.g., favorite band, style).
-
Quantitative Variables: Measure numerical values (can be continuous or discrete).
- Continuous variables: Not countable (e.g., fabric amount).
- Discrete variables: Countable (e.g., number of touchdowns).
Study Types
- Observational Study: Measures response variable without influencing it.
- Experiment: Involves manipulating an explanatory variable to observe effects.
Confounding Variables
- Confounding: When effects of multiple explanatory variables cannot be separated, leading to unclear relations.
- Lurking Variable: Not considered but affects the response.
- Confounding Variable: Included in the study, effects are indistinguishable from other variables.
Sampling Methods
- Representative Sample: Critical for valid inferential statistics.
- Simple Random Sampling: Each member has an equal chance of selection.
- Cluster Sampling: Groups are randomly selected and all within those groups are sampled.
- Systematic Sampling: Selecting every kth member from a list.
- Convenience Sampling: Utilizing easily accessible members, often biased.
Bias in Studies
- Nonresponse Bias: Exists when individuals do not respond, skewing results.
- Sampling Bias: Arises from selecting non-representative groups.
- Response Bias: Results influenced by how questions are asked or by who administers the survey.
Data Representation
- Frequency Distribution: Lists occurrences of data categories.
- Relative Frequency Distribution: Lists proportions of occurrences.
- Bar Graph: Visual representation of frequencies in bars.
- Pareto Chart: A bar graph in decreasing order of frequency.
- Histogram: For representing numerical data, suitable for large data sets.
Survey Examples
- Assessment involving various demographics (e.g., teenagers’ concert attendance).
- Comparison of preferences between subjects (students’ class preferences).
- Evaluating the response rate and its implications on data validity.
Experimental Design
- Treatment: Condition applied to experimental units.
- Response Variable: Outcome measure in an experiment.
- Double-Blind Experiment: Neither subjects nor researchers know the assigned treatments.
Statistical Evaluations
- Outliers: Sample values significantly differ from others, which can affect statistics.
- Class Limits: Define categories for grouping data in frequency distributions.
- Class Width: The difference between consecutive lower class limits.
Overall Insights
- Sales and prices data should be evaluated over time for trends and changes.
- The suitability of different charts depends on data types being analyzed (histograms for numerical, bar charts for categorical).
- Understanding the type of study and sampling method is crucial for valid conclusions in statistics.### Graph Misleading Information
- Afternoon hours have the highest robbery rates according to a misleading newspaper graph.
- Time intervals in the graph are not uniform, distorting the visual representation of data.
- To improve accuracy, intervals should be standardized for better clarity.
Graph Improvements
- Length of graph bars may favor disproportionate representations.
- Adjusting bar heights and ensuring a consistent scale can enhance the graphic's integrity.
Ideal Family Size Graph
- A bar graph is used to illustrate survey results on ideal family size.
- The graphic inadequately represents data, suggesting an alternative display like a stem-and-leaf plot would be more effective.
- Vague responses from those unaware of their ideal family size create ambiguity.
Poor Chart Representation
- A chart depicting Valentine's Day spending lacks a vertical axis, undermining data interpretation.
- Visual elements like candy boxes are considered chartjunk, distracting from the actual data.
- Absence of units adds to the inappropriate presentation of statistics.
Electricity Price Graphs
- A well-constructed graph accurately reveals trends in kilowatt-hour prices from 2003 to 2010.
- A poorly designed graph fails by not starting the vertical axis at zero, misleading viewers about price changes.
Chart Comparison
- Improved charts often feature titles and labeled axes, enhancing comprehension.
- Clear labeling aids in understanding the data better than unlabelled alternatives.
Pictograms and Data Representation
- Use of pictograms for categorical variables can lead to confusion and misinterpretation.
Data Distribution
- A right-skewed histogram indicates that the mean is likely higher than the median due to extreme values on the right.
- The mode of a dataset can be variable, not necessarily one.
Measure of Central Tendency
- Median is the preferred measure for describing candy weight due to its resilience against outliers.
- Means are significantly affected by extreme data points, making them less reliable.
Z-Score and Quartiles
- Z-scores represent how many standard deviations an observation deviates from the mean.
- Quartiles segment data into four equal parts, allowing better data analysis.
Height and Standard Deviation
- A comparison of heights shows a male at 75 inches has a z-score of 1.80, while a female at 70 inches has a z-score of 1.55.
- The male is relatively taller as his z-score indicates a larger deviation from the mean than the female's.
Standardized Tests
- A minimum score of 348 is required for admission to a selective boarding school, calculated using mean and standard deviations.
Percentiles
- A score in the 78th percentile indicates performance above 78% of examinees.
Quartile and Z-Score Statements
- The second quartile equals the median, affirming its relevance in data analysis.
- A z-score of 0 indicates values equal to the mean, contradicting the claim that such a score is impossible.
Correlation Coefficient
- A linear correlation coefficient of 0.85 indicates a strong positive relationship between variables.
Explanatory and Response Variables
- In a study about absences and final grades, absences are the explanatory variable, while the number of prescriptions in pediatric studies is the response variable.
Influence of Observations
- Influential observations can distort regression line graphs, skews the representation to favor the observation's value, thereby altering outcomes.
Living Situations of Newlyweds
- Marginal frequency calculations can provide insights into the living arrangements of newlyweds, revealing income correlations with living situations.
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