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Statistical Analysis and Interpretation of Data: Measures of Central Tendency, Variability, and Distribution

Explores statistical measures such as mean, variance, and distribution.

Andrew Taylor
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Statistical Analysis and Interpretation of Data: Measures of CentralTendency, Variability, and DistributionAnswer the following problems showing your work and explaining (or analyzing) yourresults.1.The math grades on the final exam variedgreatly. Using the scores below, how many scoreswere within one standard deviation of the mean? How many scores were within two standarddeviations of the mean?993486577385919346968879688589From the given data we can see that the sample mean is 77.93 and sample standard deviation is19.03 so if the scores are within one standard deviation of the mean they should be in the interval(77.93-19.03, 77.93+19.03) = (58.9,96.96) and we can see that 11 scores are in that interval.For 2 standard deviation of the mean the interval is = (77.93-2*19.03, 77.93+2*19.03) = (39.87,115.99) and we can see that 14 scores are in that interval.2.The scores for math test #3 were normally distributed. If 15 students had a mean score of74.8% and a standard deviation of 7.57, how many students scored above an 85%?Note that,P(X>85) = Pቀ𝑍>85−74.87.57ቁ=𝑃(𝑍>1.35)=1−𝑃(𝑍<1.35)=1−0.9115=0.0885So only 8.85% of the students has score over 85% thus the number of students =15*0.0885=1.33.3.If you know the standard deviation, how do you find the variance?The variance of a distribution is nothing but the square of its standard deviation so if I know thatstandard deviation I would just square that to get the variance.4.To get the best deal on a stereo system, Louis called eight appliance stores and asked for thecost of a specific model. The prices he was quoted are listed below:$216$135$281$189$218$193$299$235Find the standarddeviation.

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Statistics

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