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University of Alberta *

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Statistics

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Feb 20, 2024

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4) tables DESIGN Seal Orca Penguin MEAN 58.10714286 59.875 62.7143 STD. DEV. 3.447052264 2.12038 2.944 MODE 55.5 57.4 62.6 RANGE 12.4 8 11.7 Use the Descriptive Statistics tool (Lab 1 Instructions) to calculate the mean, standard deviation, mode, and range of speed for each design. Provide these values in the provided clear, organized table. Compare the means and standard deviations of the three distributions. Compare the modes and ranges of the three distributions. For the modes and ranges, are the conclusions consistent with the analysis from Question 2, part (c)? mode in a data set is basically the highest frequency value or the most repeated value From table A it clearly shows that mean gradually increases from seal moving towards the design of the penguin. The mean increases because as you go down the designs the speeds generally increase with more number of higher speeds mean gradually increases The mode also increases from seal to penguin as the value that keeps repeating in a data set is bigger. Or more repeating values have higher speed in general The range decreases as the maximum stays almost similar but the minimum keeps decreasing so the difference between max and minimum gives a smaller value Comparing it to 2c) the mode for the histograms increase then decrease but are relatively almost the same 3,4,3 But for the mode here it gradually increases from 55.5 to 62.6 indicating a slight difference in how the modes change Standard deviation shows spread across the mean and higher standard deviation means more spread across the average value in comparison the seal has the highest gradually progressing down to the penguin design. Shows consistency with design as in the histograms the seal has the most spread across the mean DESIGN Seal Orca Penguin MIN 54.4 55.9 55.1 Q1 55.5 58.3 61.4 MEDIAN 57.2 60.1 63 Q3 59.275 61.6 64.95 MAX 66.8 63.9 66.8 IQR 3.775 3.3 3.55 Use the Insert Function feature (Quartile.Inc) to compute the 5-number summary – minimum, first (lower) quartile, the second quartile (median), third (upper) quartile, and maximum – as well as

the interquartile range of speed for each design. Provide these values in the provided clear, organized table. Does the 5-number summary for each design show consistency with your conclusions about the shape of the corresponding distributions in Question 2 and 3? Explain briefly The 5 no summary as given above Yes, the corresponding data matches together and the shapes correspond with each other for example the histograms and box and whisker plots as each of the designs are either symmetrical, left skewed or right skewed. In both the graphs the seal is right skewed, orca is symmetrical and penguin is left skewed. As far as the medians and interquartile ranges go they match with the data given above for example in the 5 number summary above the mean for seal is 58.1 and the mean I calculated for the seal histogram is 58 indicating the values hence the shapes correspond to the values mode also matches as I calculated 56 from the graphs and the 5 number summary was 55.5 as the mode. For orca the mean was 59.89 and from the 5 number summary the mean was 59.88 which is very close the mode was 60 which is approximately close to 57-58. For the penguin design the mean was 64 and mode was 63.5 which almost matches the descriptive stats table of 63 and 63 as the mode and mean respectively. The ranges from the histogram were 13,8 ,11 amd from the table it was 12.4,8 ,11.7. this shows that if we use the table to plot the graph it will take the exact same shape of the histogram and box and whisker plot. The maximum and minimum and median values are also the same Seal- orca- penguin- 67- max- min -56 , 64- max- min – 56 , 67 max and 56 min Median values- seal- orca – penguin- 58,59.7,63 IQR from box and whisker- seal – orca- penguin- 4, 3.3, 3.4 This shows that since all the values match the shapes correspond . Standard deviation measures spread across the mean and according to the table data the seal has the highest spread across the mean 3.44 High IQR for the box and whisker also shows a high spread around the mean value in this case the seal design has the highest IQR progressively reducing to the penguin design Shows consistency as In the box and whisker plot the seal has the most variance across the mean MASS MEAN STD. DEV. MEAN CHANGE 575.0 64.833 3.2347 0 580.0 64.967 1.801 0.134 585.0 64.833 0.8082904 -0.134 590.0 63.7 1.2288206 -1.133 595.0 62.06667 1.9035055 -1.63 600.0 61.96667 1.9035055 -0.1 605.0 62.33333 2.9022979 0.37 610.0 62.6 3.3060551 0.27 615.0 61.26667 2.9263174 -1.33 620.0 61 1.9 -0.26 625.0 61.5 2.9866369 0.5 630.0 61.43333 3.8991452 -0.07 635.0 59.76667 1.8610033 -1.66 640.0 59.53333 1.9139836 -0.24

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