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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.

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    Statistical Analysis and Interpretation of Data: Measures of Central Tendency, Variability, and Distribution Answer the following problems showing your work and explaining (or analyzing) your results. 1. The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? 99 34 86 57 73 85 91 93 46 96 88 79 68 85 89 From the given data we can see that the sample mean is 77.93 and sample standard deviation is 19.03 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 of 74.8% and a standard deviation of 7.57, how many students scored above an 85%? Note that, P(X>85) = P ቀ 𝑍 > 85 βˆ’ 74 . 8 7 . 57 ቁ = 𝑃 ( 𝑍 > 1 . 35 ) = 1 βˆ’ 𝑃 ( 𝑍 < 1 . 35 ) = 1 βˆ’ 0 . 9115 = 0 . 0885 So 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 that standard 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 the cost of a specific model. The prices he was quoted are listed below: $216 $135 $281 $189 $218 $193 $299 $235 Find the standard deviation.

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