Homework Assignment 3

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University of Northern Iowa *

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Statistics

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Feb 20, 2024

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Lashawna Armstrong 6-23-2023 Stats assignment #3 Complete questions : 2.140, 3.18, 3.60, 3.93, 3.120, 3.132, 3.168, and 3.224b. 2.140: The graph provided is right skewed. 3.18: A: Find n. n= 4 B: sum all of the n(4) observations = 46 C: 11.5 3.60 Darts : Which player board represents data with a smaller sample standard deviation? A smaller standard deviation means a smaller spread in the data. Here it shows that for tracy the darts are almost similar distances from the center and for joan the variation of the distance from the center ranges from almost 0 to the end of the board thus having a higher range of values and a higher standard deviation. Tracey has a smaller standard deviation. 3.93: A: Compute the sample standard deviation of each of the two data sets. Sample standard deviation of dataset 1 is 6.58 and for dataset two it is 1.89 B: Compute the range of each of the two datasets. Range of dataset 1 is 24 because 24-0= 24 and dataset 2 is 7 because 17-10=7. C: What effects do outliers have on variation? Variance and standard deviation are sensitive to outliers. A single outlier can raise the standard deviation and also distort the spread. As an example, dataset 1 has a few extreme values ( 0 and 24) which raises variation (6.58). Since we found no outliers in dataset 2 the standard deviation is way lower than 1.89.

3.120: A 68% observation lies between 7 & 13 B: 95% observation lies between 4 & 16 C: 99.7% observation lies between 1 & 19 3.132 Exam scores : A- 100(1-¼) = 75% The percentage of the observations that lie within two standard deviations to either side of the mean with that given by 75%. B: 100(1-1/9) %= 88.89 % The percentage of observations that lie within three standard deviations to either side of the mean are given by 88.89%. C: The percentage of data that falls within 3 standard deviation in part b is greater than the percentage calculated in part a (chebyshev’s rule). 3.168 Parenting grandparents : A: obtain and interpret the quartiles Q1=(n-1) 0.25=15*0.25= 3.75 Q1= 4.4 Q3= n+1 *0.75 = 15*0.75 = 11.25 Q3= 5.8+(5.9-5.8)*0.25= 5.8+0.¼=5.8+0.025 5.825 B:determine and interpret the interquartile range IQR=Q3-Q1-5.825-4.4= 1.425 C:Find and interpret the five number summary Min=4, Q1=4.4, Q2=5 , Q3- 5.825, Max= 6.5 D: Identify potential outliers Lower fence Q1= 2.2625 and lower fence for Q3= 7.9625. No outliers because all of the values are within lower and upper fence. E: Construct and interpret a box plot

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