Statistics Chapter 3 Quiz
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Questions and Answers

What is a box and whisker plot?

A graphical display showing the relative position of a distribution's three quartiles as a box on a number line, along with the minimum and maximum values.

What is categorical data?

Data that are described as a category or label.

What does Chebyshev's theorem state?

Regardless of whether a distribution is bell-shaped, at least 94% of data values will fall within +/- three standard deviations of the mean, and at least 75% of data values will fall within +/- two standard deviations of the mean.

What is the coefficient of variation?

<p>A measure of the standard deviation in terms of its percentage of the mean, useful to compare the degree of variation from one data series to another.</p> Signup and view all the answers

What is the empirical rule?

<p>A rule which states that if a distribution follows a bell-shaped, symmetrical curve centered around the mean, approximately 68%, 95%, and 99.7% of the values fall within one, two, and three standard deviations around the mean, respectively.</p> Signup and view all the answers

What does the five number summary consist of?

<p>A list that consists of a distribution's minimum value, first, second, and third quartiles, and maximum value.</p> Signup and view all the answers

What is an index point?

<p>The index point, i, marks the middle of the data values and is used to determine the position of the median in the data set.</p> Signup and view all the answers

What is the interquartile range (IQR)?

<p>The difference between the first and third quartiles, corresponding to the data in the middle 50% of the range.</p> Signup and view all the answers

What is a left-skewed distribution?

<p>The shape of the distribution when the median is higher than the mean.</p> Signup and view all the answers

What is the mean?

<p>A measure of central tendency calculated by adding up all of the values in a data set and dividing by the number of observations.</p> Signup and view all the answers

What are measures of central tendency?

<p>Measures that use a single value to describe the center point of a data set.</p> Signup and view all the answers

What are measures of relative position?

<p>Measures that compare the position of one value in relation to other values in a data set.</p> Signup and view all the answers

What are measures of variability?

<p>Measures that determine how much of a spread there is within a data set.</p> Signup and view all the answers

What is the median?

<p>The value in a data set for which half the observations are higher and half are lower.</p> Signup and view all the answers

What is the midpoint?

<p>The halfway point in a set of data, found by taking the average of the endpoints for each class.</p> Signup and view all the answers

What is the mode?

<p>The value that appears most often in a data set.</p> Signup and view all the answers

What are outliers?

<p>Values that are much higher or lower than most of the data.</p> Signup and view all the answers

What are percentiles?

<p>Measures the approximate percentage of values in the data set that are below the value of interest.</p> Signup and view all the answers

What is percentile rank?

<p>Identifies the percentile of a particular value within a set of data.</p> Signup and view all the answers

What is the Pth percentile?

<p>The approximate percentage of values in the data set that are below the value of interest (where p is any number between 1 and 100).</p> Signup and view all the answers

What are quartiles?

<p>The first, second, and third quartiles are the 25th, 50th (median), and 75th percentiles.</p> Signup and view all the answers

What is range?

<p>A measure of variability found by subtracting the lowest value from the highest value in a data set.</p> Signup and view all the answers

What are right-skewed distributions?

<p>The shape of a distribution when the mean is higher than its median.</p> Signup and view all the answers

What is the sample correlation coefficient (rxy)?

<p>Measures both the strength and direction of the linear relationship between two variables.</p> Signup and view all the answers

What is standard deviation?

<p>The square root of a distribution's variance.</p> Signup and view all the answers

What is variance?

<p>A measure of variation that describes the relative distance between the data points in a set around the mean of the data set.</p> Signup and view all the answers

What is a weighted mean?

<p>Allows you to assign more weight to certain values and less weight to others when calculating the mean.</p> Signup and view all the answers

What is a z-score?

<p>A measure that identifies the number of standard deviations a particular value is from the mean of its distribution.</p> Signup and view all the answers

Study Notes

Box and Whisker Plot

  • Displays the relative position of a distribution's quartiles and its minimum and maximum values on a number line.

Categorical Data

  • Comprises data described in categories or labels rather than numerical values.

Chebyshev's Theorem

  • States that at least 94% of data values lie within +/- three standard deviations of the mean, and at least 75% fall within +/- two standard deviations, applicable to any distribution.

Coefficient of Variation

  • Represents the standard deviation as a percentage of the mean, useful for comparing variance between different data sets.

Empirical Rule

  • Pertains to bell-shaped distributions, indicating that approximately 68%, 95%, and 99.7% of values fall within one, two, and three standard deviations from the mean, respectively.

Five Number Summary

  • Consists of five values: minimum, first quartile, median (second quartile), third quartile, and maximum.

Index Point

  • Marks the median's position in the data set by identifying the middle value among the observations.

Interquartile Range (IQR)

  • Calculated as the difference between the first and third quartiles, it represents the range of the middle 50% of the data.

Left-Skewed Distribution

  • Characterized by a median that is higher than the mean, indicating a tail on the left side of the distribution.

Mean

  • A central tendency measure calculated by dividing the sum of all values in a data set by the number of observations.

Measures of Central Tendency

  • Values used to represent the center of a data set, including mean, median, and mode.

Measures of Relative Position

  • Evaluate how a particular value compares in relation to the other values within the data set.

Measures of Variability

  • Assesses the spread or dispersion of data points within a data set, including range and standard deviation.

Median

  • The middle value in a data set, where half of the observations are above and half are below.

Midpoint

  • The average of the endpoints within each class in a data set, used for classifying data.

Mode

  • Represents the most frequently occurring value within a data set.

Outliers

  • Data points that significantly deviate from the rest of the data, appearing much higher or lower than the majority.

Percentiles

  • Indicate the approximate percentage of values in a data set that fall below a specific threshold value.

Percentile Rank

  • Identifies the percentile corresponding to a particular value, indicating its position relative to the entire set.

Pth Percentile

  • Defines the percentage of data points below a given value p (where p ranges from 1 to 100).

Quartiles

  • Specifically refer to the first (25th), second (50th, median), and third (75th) quartiles, dividing the data into four equal parts.

Range

  • A measure of variability derived from subtracting the lowest data point from the highest.

Right-Skewed Distribution

  • A distribution shape where the mean exceeds the median, indicating a longer tail on the right.

Sample Correlation Coefficient (rxy)

  • Measures the strength and direction of a linear relationship between two variables, helping to assess correlation.

Standard Deviation

  • The square root of the variance, quantifying the amount of variation or dispersion in a set of values.

Variance

  • A statistical measure detailing the spread of data points around the mean, reflecting how far individual values deviate from it.

Weighted Mean

  • A mean calculation that incorporates different weights for various values, allowing for more nuanced analysis.

Z-Score

  • Indicates how many standard deviations a specific value is from the mean, facilitating comparison across different distributions.

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Test your understanding of key concepts in statistics with this Chapter 3 quiz. Explore important terms like box and whisker plots, categorical data, and Chebyshev's theorem. Perfect for students looking to reinforce their knowledge.

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