Math 125Q Quiz 1
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Which average represents the middle value of a data distribution?
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median
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Which average represents the most frequent value of a data distribution?
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mode
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Which average takes all the specific values into account?
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mean
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What symbol is used for the arithmetic mean when it is a sample statistic?
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statistic, x bar
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What symbol is used when the arithmetic mean is a population parameter?
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parameter, ?
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When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median, and mode?
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The mean, median, and mode are approximately equal.
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Identify all the averages (mean, median, or mode) that can be used to summarize the data. (a) Outstanding balance on each account. (b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.). (c) Dollar amount due on next payment.
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(a) mode, median, mean (b)mode (c)mode, median, mean
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If the highest number were increased, what would be the effect on the median and mean?
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The mean would increase while the median would remain the same.
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If the highest number were decreased to a value still larger than B, what would be the effect on the median and mean?
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The mean would decrease while the median would remain the same.
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If the highest number were decreased to a value smaller than B, what would be the effect on the median and mean?
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Both the mean and median would decrease.
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Which average - mean, median, or mode - is associated with the standard deviation?
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mean
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What is the relationship between the variance and the standard deviation for a sample data set?
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The standard deviation is the square root of the variance.
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When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population?
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Yes. The formula for s is divided by n ? 1, while the formula for ? is divided by N
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What symbol is used for the standard deviation when it is a sample statistic?
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Sample statistic: s
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What symbol is used for the standard deviation when it is a population parameter?
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Population parameter: ?
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(i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) Without doing any computations, order the data sets according to increasing value of standard deviations. (b)Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)?
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(a)(i), (ii), (iii) (b)The data change between data sets (i) and (ii) increased the squared difference ?(x - x)2 by more than data sets (ii) and (iii).
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One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?
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(a)No, since 80 is less than 2.5 standard deviations above the mean. (b)Yes, since 80 is more than 2.5 standard deviations above the mean.
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Angela took a general aptitude test and scored in the 86th percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score? (b) What percentage were above?
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(a) 86% (b) 14%(b)
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One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?
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75%
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The town of Butler, Nebraska, decided to give a teacher-competency exam and defined the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0 to 100. Was a raw score of 82 necessarily a passing score?
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No, it might have a percentile rank less than 70.
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Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy?
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Timothy, since his percentile score is higher.
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To find median:
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Order data, find middle value or if two, add them and divide by two
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Does median usually change if extreme data values change?
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No
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Median equation for a lot of data
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n + 1 / 2
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?x
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the sum of all given values
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x bar
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sample mean
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?
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population mean
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n
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number of data values in sample
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N
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number of data values in population
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Can the mean be affected by exceptional values?
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yes, it is not a resistant measure
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Weighted average formula
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Weighted mean = ?wx/?w ? = the sum of w = the weights x = the value
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Range
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largest value- smallest value
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Sample standard deviation- defining formula
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find the mean subtract the mean from column 1 square each value in column 2 and add them up to get sample variance: divide the sum of column 3 by n-1 to get standard deviation: take the square root of the variance
