Chapter 03 - Describing Data: Numerical Measures75. A purchasing agent for a trucking company is shopping for replacement tires for theirtrucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tireshave an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B'stires have an average life of 60,000 miles with a standard deviation of 2,000 miles.Which of the following statements is true?A.The two distributions of tire life are the sameB.On average, Supplier A's tires have a longer life then Supplier B's tiresC.The life of Supplier B's tire is more predictable than the life of Supplier A's tiresD.The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire lifeAACSB: Reflective Thinking SkillsBLOOM: AnalysisDifficulty: MediumGoal: 476. The sum of the differences between sample observations and the sample mean isA.ZeroB.The mean deviationC.The rangeD.The standard deviationAACSB: Communication AbilitiesBLOOM: ComprehensionDifficulty: EasyGoal: 477. What are the disadvantage(s) of the mean deviation?A.It is based on only two observationsB.It is based on deviations from the meanC.It uses absolute values, which are difficult to manipulateD.It is only applied to skewed distributions.AACSB: Communication AbilitiesBLOOM: ComprehensionDifficulty: MediumGoal: 53-54 Show Solution : The disadvantage of using range is that it does not measure the spread of the majority of values in a data set-it only measures the spread between highest and lowest values. As a result, other measures are required in order to give a better picture of the data spread. The range is obtained by subtracting the smallest observation from the highest in the data. So, the range is based on two extreme observations, and it is not biased by a large mean. The range is estimated based on only two observations in the data, not all of them. As a result, it is not a reliable indicator of dispersion. The range's unit is the same as the original data's unit. As a result, the range's measurement unit is not considered a disadvantage. Hence, the only disadvantage is that it depends on only 2 observations. Answer: (a) One of the greatest disadvantages of using range as a method of dispersion is that range is sensitive to outliers in the
data. Range only considers the smallest and largest data elements in the set. If outliers exist in a set of data such that the lowest or highest extremes are far away from almost every other data element in the set, then range may not be the best way to measure dispersion. For example, if one were to measure a student’s consistency on quizzes, and he scored {40, 90, 91, 93, 95, 100} on six different quizzes, the range would be 60 points, marking considerable inconsistency.
However, five of the six quizzes show consistency in the student’s performance, achieving within 10 points of each other on all of these. Using other methods of dispersion, such as measuring the interquartile range, the difference between the 25th and 75th percentile, provide a better representation of dispersion in cases where outliers are involved. Standard deviation and average deviation are also commonly used methods to determine the dispersion of data. MORE
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What is a disadvantage of the range as a measure of dispersion quizlet?What is a disadvantage of the range as a measure of dispersion? It is based on only two observations.
What are the disadvantages of dispersion?Demerits. It is not based on all the observations.. It is not capable of further algebraic treatment or statistical analysis.. It is affected considerably by fluctuations of sampling.. It is not regarded as a very reliable measure of dispersion because it ignores 50% observations.. What is a disadvantage of the range as a measure of dispersion based on only two observations?Answer and Explanation:
It gives two values, which is the highest and the lowest value of the dataset. This is the biggest disadvantage of range and hence is not the preferred metric for measuring dispersion in the data set.
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Which of the following is a major disadvantage of the range as a measure of dispersion?
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