Exam 2: Describing Data: Numerical

Questions concerning the location or position of a value relative to the entire set of data are answered by examining measures of location such as percentiles and quartiles.

The Empirical rule applies to any distribution,regardless of its shape,as an interpretive guide to the distribution.

According to the Empirical Rule,the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution)that should fall within two standard deviations of their mean is approximately:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A set of data is mounded,with a mean of 500 and a variance of 576. -Approximately what proportion of the observations is less than 548?

How well does the Empirical Rule work for the fraction of data actually falling within ± one standard deviation of the mean?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following (x,y)sample data: (24,24),(19,33),(21,31),(10,36),(22,30),(13,36),(21,32),(23,26),(20,26),and (21,31). -Compute and interpret b₁;the slope of the least squares regression line.

For any set of grouped or ungrouped data,which measures of central location always have only one value?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Calculate the following sample observations on fracture strength: 128,131,142,168,87,93,105,114,96,and 98. -Calculate and interpret the value of the sample mean

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The police lieutenant in charge of the traffic division has reviewed the number of traffic citations issued per day by each of the 10 police officers in his division.The data were: 13,21,12,34,31,13,22,26,25,and 23. -What is the third quartile of the number of citations issued per day?

The interquartile range is very unique in the sense that it is a measure of central tendency as well as a measure of dispersion.

What conclusions can you draw about the relationship between age and net wealth?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sample of 33 students was asked to rate themselves on whether they were outgoing or not using this five point scale: 1 = extremely extroverted,2 = extroverted,3 = neither extroverted nor introverted,4 = introverted,or 5 = extremely introverted.The results are shown in the table below: -Calculate the sample standard deviation.

For the sample data shown below,compute the five-number summary,and sketch out the Box-and-Whisker plot.

Measures of central tendency provide information about atypical observations in data.

The measures that indicate the location or positions of a value relative to the entire set of data are called the:

Suppose you are told that the average return on investment for a particular class of investments was 7.8% with a standard deviation of 2.3.Furthermore,the histogram of the distribution of returns is approximately bell-shaped.We would expect that 95 percent of all of these investments had a return between what two values?

Which of the following statements is true?

For any distribution,the percent of observations that lie within four standard deviations of the mean is:

The following subscripted xs represent a sample of size n = 67 which has been ranked from smallest (x₁)to largest (x₆₇): x₁,x₂,x₃,…x₆₅,x₆₆,x₆₇.Prepare a 5-number summary for this sample in terms of the subscripted xs.

Why do we have so many different measures of central tendency? Are all really necessary or do they essentially provide the same information?