Questions and Answers
What is a percentile?
The pth percentile of a distribution is the value with p percent of the observations less than it.
What is a cumulative relative frequency graph?
A cumulative relative frequency graph displays the cumulative relative frequency of each class of a frequency distribution.
What is an ogive?
A cumulative relative frequency graph.
Where is the mean of a density curve?
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Where is the median of a density curve?
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What is Normal distribution?
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What is a z-score?
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What is the standard normal distribution?
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What relationships do positive and negative z-scores show?
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When assessing a problem, what is the first thing to do?
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What effect does adding/subtracting a constant do to the data?
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What specifically remains the same when adding/subtracting constants to data?
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What effect does dividing/multiplying by a constant do to the data?
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What specifically remains the same when dividing/multiplying constants to data?
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What does a linear transformation do to the data?
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What should you always contain when writing about quantitative data?
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What is a density curve?
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How should you describe a density curve?
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Where do the mean and median fall on a skewed density curve?
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What are two ways of describing an individual's location within a distribution?
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How do we examine an individual's location within a distribution?
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What is good about a density graph?
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What does theta represent?
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What does p-hat represent?
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What does mu represent?
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What does x-bar represent?
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What does sigma represent?
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What does s represent?
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What is the difference between the parameter & the statistic?
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All normal curves are ______, ______, and ______.
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Are normal curves density curves?
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Is it possible to state that a curve from data is normally distributed?
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What does a steep peak of a normal distribution mean?
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What does a wide peak of a normal distribution mean?
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How is the normal distribution abbreviated?
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What are good examples for normally distributed data in the real world?
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What is the empirical rule?
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Study Notes
Percentiles and Graphs
- A percentile indicates the value below which a percentage of observations fall.
- Cumulative relative frequency graphs represent the accumulation of relative frequency for a distribution.
- An ogive is another term for a cumulative relative frequency graph.
Density Curves
- The mean of a density curve represents the balance point of the curve.
- The median is the point that divides the area under the curve into two equal halves.
- Normal distribution is defined by a mean (μ) and a standard deviation (σ), abbreviated as N(μ, σ).
Z-Scores
- A z-score standardizes an observation by calculating how many standard deviations it is from the mean: z = (x - mean) / standard deviation.
- A standard normal distribution specifically has a mean of 0 and a standard deviation of 1.
- Positive z-scores indicate values above average, while negative z-scores indicate values below average.
Data Assessment Techniques
- Initial assessment of data involves checking for skewness or normal distribution.
- Adding or subtracting a constant shifts the center without changing the shape or spread of the data.
- Measures such as the number of data points, standard deviation, IQR, range, and distribution shape remain unchanged when constants are added or subtracted.
Effects of Linear Transformations
- A linear transformation adjusts a variable via an equation: x-new = a + bx, where 'a' is a constant added and 'b' is a multiplier.
- Dividing or multiplying data by a constant retains the shape but alters measures of center and spread proportionally.
Describing Distributions
- A density curve features an area of 1 and is always non-negative.
- Median is the equal-areas point, and the mean is the balance point of the density curve.
- On skewed curves, the mean is pulled toward the long tail, affecting its relationship with the median.
Location and Proportions
- Individual placement within a distribution can be described using percentiles and z-scores.
- Cumulative relative frequency graphs effectively illustrate an individual's location in a distribution.
Statistical Notations
- Symbols include θ for population proportion, p-hat for sample proportion, μ for population mean, x-bar for sample mean, σ for population standard deviation, and s for sample standard deviation.
- Parameters pertain to entire populations, while statistics pertain to samples.
Normal Distribution Characteristics
- Normal curves are symmetric, single-peaked, and bell-shaped.
- All normal curves function as density curves but asserting a dataset as normally distributed should be stated as "approximately" normal.
- A steep normal distribution peak indicates a smaller standard deviation, while a wider peak indicates a larger standard deviation.
Empirical Rule
- The empirical rule outlines probability distributions in normal data: approximately 68% within ±1 standard deviation, 95% within ±2 standard deviations, and 99.7% within ±3 standard deviations from the mean.
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Description
This quiz provides a comprehensive review of Chapter 2 in AP Statistics. It covers key concepts such as percentiles, cumulative relative frequency graphs, and ogives. Test your understanding and reinforce your knowledge with these flashcards.