AP Stats Chapter 2 Review

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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?

The point at which the curve would balance if made of solid material. Signup and view all the answers

Where is the median of a density curve?

The point with half the area under the curve to its left and the remaining half of the area to its right. Signup and view all the answers

What is Normal distribution?

Described by a Normal density curve. Any particular Normal distribution is specified by its mean μ and standard deviation σ. Signup and view all the answers

What is a z-score?

If x is an observation from a distribution that has known mean and standard deviation, the standardized value of x is z = (x - mean) / standard deviation. Signup and view all the answers

What is the standard normal distribution?

The normal distribution with mean 0 and standard deviation 1. Signup and view all the answers

What relationships do positive and negative z-scores show?

A positive z-score means the point is above average, and a negative z-score means that point is below average. Signup and view all the answers

When assessing a problem, what is the first thing to do?

Find out whether the data is skewed or normally distributed. If so, write it down and explain why. Signup and view all the answers

What effect does adding/subtracting a constant do to the data?

The shape remains the same, the center & other measures of location increase/decrease by whatever was added/subtracted, and the measures of spread stay the same. Signup and view all the answers

What specifically remains the same when adding/subtracting constants to data?

<ol> <li>The amount of data points 2. The standard deviation 3. The IQR 4. The range 5. The shape of the distribution.</li> </ol> Signup and view all the answers

What effect does dividing/multiplying by a constant do to the data?

If each data point was multiplied/divided by B, then the shape remains the same while measures of spread are multiplied/divided by B. Signup and view all the answers

What specifically remains the same when dividing/multiplying constants to data?

The shape of the distribution. Signup and view all the answers

What does a linear transformation do to the data?

A linear transformation changes the original variable x into the new variable x-new given by an equation of the form: x-new = a + bx. Signup and view all the answers

What should you always contain when writing about quantitative data?

<ol> <li>Always plot your data, make a graph 2. Look for the overall pattern (shape, center, spread) and for striking features such as outliers. 3. Calculate the numerical summary to describe center and spread.</li> </ol> Signup and view all the answers

What is a density curve?

A density curve is a curve that is always on or above the horizontal axis and has area exactly 1 underneath it. Signup and view all the answers

How should you describe a density curve?

Use measures of center and spread: the median is the equal-areas point, and the mean is the balancing point. Signup and view all the answers

Where do the mean and median fall on a skewed density curve?

The mean is pulled away from the median in the direction of the tail; it is greater than the median if skewed left and vice versa. Signup and view all the answers

What are two ways of describing an individual's location within a distribution?

The percentile and z-score. Signup and view all the answers

How do we examine an individual's location within a distribution?

Use a cumulative relative frequency graph. Signup and view all the answers

What is good about a density graph?

It is an idealized description of a distribution that smooths out the irregularities in the actual data. Signup and view all the answers

What does theta represent?

The proportion of the total population. Signup and view all the answers

What does p-hat represent?

The proportion of the sample. Signup and view all the answers

What does mu represent?

The mean of a population. Signup and view all the answers

What does x-bar represent?

The mean of a sample. Signup and view all the answers

What does sigma represent?

The standard deviation of a population. Signup and view all the answers

What does s represent?

The standard deviation of a sample. Signup and view all the answers

What is the difference between the parameter & the statistic?

The parameter is total population, whereas the statistic is just a sample. Signup and view all the answers

All normal curves are , , and __.

symmetric, single-peaked, and bell-shaped. Signup and view all the answers

Are normal curves density curves?

True Signup and view all the answers

Is it possible to state that a curve from data is normally distributed?

False Signup and view all the answers

What does a steep peak of a normal distribution mean?

It means that there is a smaller standard deviation, meaning there are more points towards the mean. Signup and view all the answers

What does a wide peak of a normal distribution mean?

It means that there is a larger standard deviation, and that there are fewer points towards the mean. Signup and view all the answers

How is the normal distribution abbreviated?

N(μ, σ). Signup and view all the answers

What are good examples for normally distributed data in the real world?

Normal distributions are good approximations of the results of many kinds of chance outcomes. Signup and view all the answers

What is the empirical rule?

68-95-99.7% rule, in the normal distribution: approximately 68% of the observations fall within 1 standard deviation of the mean. Signup and view all the answers

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.