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# Solutions for Chapter 2-3: Frequency Distributions and Graphs

## Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition

ISBN: 9780073534978

Solutions for Chapter 2-3: Frequency Distributions and Graphs

Solutions for Chapter 2-3
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##### ISBN: 9780073534978

This textbook survival guide was created for the textbook: Elementary Statistics: A Step by Step Approach, edition: 7. Elementary Statistics: A Step by Step Approach was written by and is associated to the ISBN: 9780073534978. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2-3: Frequency Distributions and Graphs includes 33 full step-by-step solutions. Since 33 problems in chapter 2-3: Frequency Distributions and Graphs have been answered, more than 32627 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Bivariate normal distribution

The joint distribution of two normal random variables

• Block

In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

• Box plot (or box and whisker plot)

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

• Chi-square test

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Conidence coeficient

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Control limits

See Control chart.

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Experiment

A series of tests in which changes are made to the system under study

• Fraction defective control chart

See P chart

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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