Questions and Answers
What is a sample?
a subset selected to represent the population
What is a random sample?
each member of the population has an equal chance of being selected as a part of the sample
What is a self-selected sample?
members volunteer to be included in the sample
What is a convenience sample?
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What is the mean?
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What is the median?
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What are measures of central tendency?
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What is the range of a set of data?
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What is the interquartile range (IQR)?
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What are independent events?
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What is a probability distribution graph?
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What does a z-score indicate?
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What is a standard normal curve?
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What is the mode of the set of data values {6.1, 9.5, 3.8, 4.6, 6.1, 2.0, 3.7, 2.1}?
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What is the median of the set of data values {6.1, 9.5, 3.8, 4.6, 6.1, 2.3, 3.7, 2.1}?
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What is the standard deviation for the set of data values {25, 29, 21, 19, 30, 26, 28}?
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Find the margin of error (moe) for the sample proportion, given the sample size n = 300. Round to the nearest percent.
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Find the margin of error (moe) for the sample proportion, given the sample size n = 125. Round to the nearest percent.
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What is the probability that all her friends are available to meet for lunch on three different days if there is a 20% chance that all of her friends will be available?
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Estimate the percent of scores that were 90 or higher if the mean score on a quiz is 82 and the standard deviation is 4.
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Find the sample proportion (as a %) given 27 out of 60 shoppers prefer generic brands when available.
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What number of pieces of checked luggage is 3 standard deviations above the mean when the mean is 380 and the standard deviation is 20?
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Find the P(boy and reads horror stories) if 59% of respondents are girls and the percentage of boys reading horror stories is 49%.
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What is the participant's bowling score whose z-score is -2.5 if the mean bowling score is 205 and the standard deviation is 14?
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Approximately how many students receive grades of 61 or below in a university class of 174 students, if the mean score is 68.5 and the standard deviation is 7.3?
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Study Notes
Statistical Sampling Methods
- Sample: A subset chosen to represent a larger population.
- Random Sample: Every member of the population has an equal chance of selection, akin to drawing names from a hat.
- Self-Selected Sample: Participants choose themselves to be included, like customers taking a survey at a store.
- Convenience Sample: Comprises members that are easily accessible, such as students on a specific bus.
Measures of Central Tendency
- Mean: The average value calculated by summing data points and dividing by the total number of data.
- Median: The middle number in a sorted list of data values.
- Mode: The number that appears most frequently in a dataset.
Data Range and Distribution
- Range: The difference between the maximum and minimum values in a dataset.
- Interquartile Range (IQR): The difference between the third quartile (Q3) and the first quartile (Q1).
Probability Concepts
- Independent Events: Two events where the outcome of one does not influence the other.
- Probability Distribution Graph: Visual representation showing the probabilities of all possible outcomes for a random variable, with total probability summing to 1.
Statistical Measurements
- Z Score: Indicates how many standard deviations a data point is from the mean.
- Standard Normal Curve: A symmetrical bell-shaped graph representing a normal distribution, with 50% of data below the mean and 50% above.
Statistical Calculations and Applications
- Margin of Error (MOE): Reflects the potential error in sample proportions, calculated based on sample size.
- Probability Calculations: For example, for Jean, the chance of all friends being available across three days is 5.12%.
- Standard Deviation: Measures the dispersion of a dataset. For example, the standard deviation from a set of data values might be 3.81.
Contextual Data Problems
- Sample Proportion: For 27 out of 60 shoppers preferring generic brands, the sample proportion is 45%.
- Checked Luggage: 3 standard deviations above a mean of 380 luggage pieces results in 440 pieces.
- Survey Analysis: In a survey, the probability that a boy reads horror stories can be calculated based on given percentages.
- Z-Score Application: The z-score of -2.5 for bowling indicates a participant's score of 170 for a mean of 205 and standard deviation of 14.
- Exam Score Distribution: In a class with a mean of 68.5, it's estimated that approximately 28 students scored 61 or below.
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Test your knowledge with this flashcard quiz on statistics and probability concepts from Algebra 2. Each card covers key terms and definitions, helping you reinforce your understanding. Perfect for students looking to review important concepts before exams.