Exam 2: Describing Data With Numerical Measures

Thirty-three students were 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: a. Find the percentage of measurements in the following intervals: = ______________ = ______________ This interval contains approximately ______________% of the data. = ______________ = ______________ This interval contains approximately ______________% of the data. b. Comment on the shape of the distribution. ____________________________

An analytical chemist wanted to use electrolysis to determine the number of moles of cupric ions in a given volume of solution. The solution was partitioned into n = 30 portions of 0.2 milliliter each. Each of the n = 30 portions was tested. The average number of moles of cupric ions for the n = 30 portions was found to be 0.185 mole; the standard deviation was 0.015 mole. Calculate the following intervals: = ______________ = ______________ = ______________ Describe the distribution of the measurements for the n = 30 portions of the solution using Tchebysheff's Theorem. ________________________________________________________ Describe the distribution of the measurements for the n = 30 portions of the solution using the Empirical Rule. ________________________________________________________ Suppose the chemist had used only n = 5 portions of the solution for the experiment and obtained the readings 0.18, 0.21, 0.20, 0.22, and 0.18. Would the Empirical Rule be suitable for describing the n = 5 measurements? ______________ Explain. ________________________________________________________

The value of the standard deviation may be either positive or negative, while the value of the variance will always be positive or zero.

The Empirical Rule and Tchebysheff's Theorem can be used to describe data sets.

The standard deviation is a measure of relative standing.

Measures of center are values around which observations tend to cluster and that describe the location of what in some sense might be called the "center" of a data set.