prices of Baltimore Gas & Electric Company since stock prices are positively correlated to earnings as well. When the average temperature of a particular quarter is exceptionally low, one will predict that the stock prices of the company will increase in the following quarter.(c) The relationship between stock prices and average temperature should be relevant only for a subset of natural resource stocks that are closely related to the heating industry.

3.40 (a) -0.1641(b) The low coefficient of correlation between price and energy cost indicates that there is a very week negative linear relationship between the two if there is any.3.41(a) Scatter Diagram05010015020025030035005101520Fat (%)Calories(b) There appears to be a positive relationship between calories and fat content.3.42(a) 0.9864r(b) The coefficient of correlation of 0.9864 is very close to +1, which indicates that there is avery high linear positive relationship between weight of mail and the number of orders.3.43 We should look for ways to describe the typical value, the variation, and the distribution of the data within a range.3.44 Central tendency or location refers to the fact that most sets of data show a distinct tendency to group or cluster about a certain central point.

88 Chapter 3: Numerical Descriptive Measures3.45 The arithmetic mean is a simple average of all the values, but is subject to the effect of extremevalues. The median is the middle ranked value, but varies more from sample to sample than thearithmetic mean, although it is less susceptible to extreme values. The mode is the most common value, but is extremely variable from sample to sample.3.46 Measures of central tendency measure a central point in a set of data. Measures of noncentral tendency such as quartiles, measure other points in the distribution.3.47 Variation is the amount of dispersion,or “spread,” in the data.3.48 The range is a simple measure, but only measures differences between the extremes. The interquartile range measures differences in the center fifty percent of the data. The standard deviation measures variation around the mean, and is the only measures that takes into account each observation.3.49 The empirical rule relates the mean and standard deviation to the percentage of values that will fall within a certain number of standard deviation of the mean.3.50 Shape is the manner in which the data are distributed.3.51 The box-and-whisker plot and five number summary allow one to determine the approximate shape of the distribution. In addition, the box-and-whisker plot allows the comparison of several groups in terms of their location, dispersion, and shape.3.52(a) mean = 5.5014 median = 5.515(b) first quartile = 5.44third quartile = 5.57 (c) range = 0.52interquartile range = 0.13 variance = 0.0112 standard deviation = 0.106coefficient of variation = 1.924%(d) The average weight of the tea bags in the sample is 5.5014 grams while the middle ranked weight is 5.515. The company should be concerned about the central tendency because that is where majority of the weight will scatter around.(e)