Exam 4: A: Numerical Descriptive Techniques

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The coefficient of variation is a measure of variability.

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Weights of Police Officers The following data represent the weights in pounds of a sample of 25 police officers: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171. -{Weights of Police Officers Narrative} Construct a frequency distribution for the data,using five class intervals,and the value 130 as the lower limit of the first class.

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Test Scores Suppose that an analysis of a set of test scores reveals that: Q1 = 45,Q2 = 85,Q3 = 105. -{Test Scores Narrative} Calculate the interquartile range.What does this tell you about the data?

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σ\sigma is a population parameter and xˉ\bar { x } is a sample statistic.

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Pets Survey A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table. Number of Pets 0 1 2 3 4 5 Number of Families 3 20 5 4 2 2 -{Pets Survey Narrative} Determine the mean,the median,and the mode of the number of pets owned per family.

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If the observations are in the millions,a standard deviation of 10 would be considered small.If the observations are all less than 50,a standard deviation of 10 would be considered large.

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Quartiles divide the observations in a data set into four parts with the same amount of data in each part.

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The ____________________ is calculated by finding the middle of the data set,when the data are ordered from smallest to largest.

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Weights of Teachers The following data represent the weights in pounds of a sample of 25 teachers: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171. -{Weights of Teachers Narrative} Which is a better measure of variability in the weights of the teachers,the standard deviation or the coefficient of variation?

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The variance is more meaningful and easier to interpret compared to the standard deviation.

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The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell shaped distribution)that fall within two standard deviations of their mean is approximately:

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2-Year Investment Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. -{2-Year Investment Narrative} Compare the values of the arithmetic and geometric means.

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In a histogram,the proportion of the total area which must be to the right of the mean is:

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Milk Demand A supermarket has determined that daily demand for milk containers has an approximate bell shaped distribution,with a mean of 55 containers and a standard deviation of six containers. -{Milk Demand Narrative} How often can we expect between 49 and 61 containers to be sold in a day? (Give a percentage. )

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The 5-number summary consists of the smallest observation,the first quartile,the median,the third quartile,and the largest observation.

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The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.

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Ages of Volunteers The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20. -{Ages of Volunteers Narrative} Compute the sample variance and sample standard deviation,and express the numbers in the appropriate units.

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The ____________________ is the least effective of all the measures of variability.

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The 10th ____________________ is the value for which 10% of the observations are less than that value.

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Suppose that a firm's sales were $2,500,000 four years ago,and sales have grown annually by 25%,15%,-5%,and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

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