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0 500000 1500000 2500000 3500000 VALUE IN THOUSANDS b) Create and paste a boxplot that summarizes the assessed residential dwelling values for the HIGHLANDS dwellings. What can you tell about the distribution of the data? (4 marks) The bulk of the data, between Q1 and Q3, falls between about 350K to 500K (very roughly, from the boxplot). There is a short tail to the left that shows some less expensive properties were assessed and a much larger tail to the right that shows several expensive properties were assessed, including one extreme outlier at 3.5 million. In this case, the mean will be pulled above the median as there are many more outliers to the right than the lefi. HIGHLANDS ASSESSED RESIDENTIAL DWELLING VALUES 1116 o 3500000 1 2500000 | THOUSANDS 1500000 1 = o6 =~ om 500000 1988 1 0 1 ¢)Find and paste a full set of descriptive measures for the entire population of assessed HIGHLANDS residential dwelling values. Choose the most appropriate descriptive measures and explain your choice (with reference to the shape of the data distribution). (4 marks) mean sd IQR 0% 25% 50% 75% 100% n 440340.1 207868 163250 500 339625 401000 502875 3422000 1l1le6 As the data is right skewed, the median of 401K is the most appropriate measure of centrality, and the IQR of 520K-340K = 162K is the most appropriate measure of spread. 50% of the assessed home values will fall between 340K and 502K. The distance from the minimum to Q1 is quite notable (about 338K), as is the very much larger distance of about 3500K from Q3 to the maximum. The distance from Q1 to the median is about 60K, while the distance from the median to Q3 is about 101K. The mean of 440K is pulled above the median of 401K by the values of the outlying highly assessed homes. Overall, if one ignores the outlying values, one can likely get a fairly nice home for around 400K in this neighbourhood. d) You will notice that the histogram distribution of assessed residential dwelling values that you found for the Highlands in the sample of size 15 taken in Part A does not match the shape of the distribution you found when you used the HIGHLANDS datafile with the assessed dwelling values for all residential dwellings in the Highlands in Part B. Furthermore, the boxplot of assessed residential dwelling values that you found for the Highlands in the sample of size 15 taken in Part A does not match the shape of the boxplot you found when you used the HIGHLANDS datafile with the assessed dwelling values for all residential dwellings in the Highlands. State how the shapes differ and explain why this may have happened. (4 marks) The sample did not obtain any of the very high values in the dataset, but did obtain a lower value from the dataset. Thus, the small sample (size 15) ended up with a left skewed distribution in spite of the actual population of all assessed values being right skewed!! Even though it was indicated that the sample was taken randomly (as appropriate), the random