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Chapter 2 Tutorial 2nd & 3rd LAB Boxplot Example 1 Draw the boxplot For the following set 1 1 3 5 6 6 7 8 12 13 15 Min= Q1= Median= Q3= Max= IQR= 1.5×IQR= Q1- 1.5×IQR= Q2+1.5×IQR= Boxplot Example 1 Draw the boxplot For the following set 1 1 3 5 6 6 7 8 12 13 15 Min=1 Q1=3 Median=6 Q3=12 Max=15 IQR=12-3=9 1.5×IQR=13.5 Q1- 1.5×IQR=-10.5 Q3+1.5×IQR=25.5 Boxplot Example 1 16 14 12 Min=1 Q1=3 Median=6 Q3=12 Max=15 10 8 6 4 2 0 Sample 1 Boxplot Example 2 Draw the boxplot For the following set 2 3 3 6 7 7 7 9 13 15 30 Min= Q1= Median= Q3= Max= IQR= 1.5×IQR= Q1- 1.5×IQR= Q2+1.5×IQR= Boxplot Example 2 Draw the boxplot For the following set 2 3 3 6 7 7 7 9 13 15 30 Min=2 Q1=3 Median=7 Q3=13 Max=30 IQR=10 1.5×IQR=15 Q1- 1.5×IQR=-12 Q2+1.5×IQR=28 Boxplot Example 2 Min=2 Q1=3 Median=7 Q3=13 Max=30 35 30 25 20 Q1- 1.5×IQR=-12 Q2+1.5×IQR=28 15 10 5 0 Sample 1 Min Outlier Max Outlier Boxplot Example 2 Min=2 Q1=3 Median=7 Q3=13 Max=30 35 30 25 20 Terminate whiskers at the most extreme observation within 1.5×IQR of the quartiles 15 10 5 0 Sample 1 Min Outlier Max Outlier Q1- 1.5×IQR=-12 Q2+1.5×IQR=28 Q2 2) Suppose that the data for analysis includes the attribute grade. The grade values for the data tuples are: 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (a) What is the mean of the data? What is the median? • Using Equation (2.3), the mean = 13.61 • The median = (13+14)/2 = 13.5 Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (b) What is the mode of the data? Comment on the data's modality (i.e., bimodal, trimodal, etc.). • The mode (value occurring with the greatest frequency) of the data is 13, the mode is only one value so it’s called unimodal. Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (c) What is the midrange of the data? • The midrange (average of the largest and smallest values in the data set) of the data is: • (20+ 4) / 2 = 12 Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (d) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data? • The first quartile (corresponding to the 25th percentile) of the data is: 12. The third quartile (corresponding to the 75th percentile) of the data is: 17. Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (e) Give the five-number summary of the data. • The five number summary of a distribution consists of the minimum value, first quartile, median value, third quartile, and maximum value. It provides a good summary of the shape of the distribution and for this data is: 4,12,13.5,17,20 Q2 4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20 (f) Show a boxplot of the data. 25 20 15 10 5 0 Sample 1 Min Outlier Max Outlier Q3 3) Suppose that the data for analysis includes the attribute age. The age values for the data tuples are 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (a) What is the mean of the data? What is the median? • Using (Equation 2.1), the (arithmetic) mean of the data is: = 809/27 = 30. The median (middle value of the ordered set, as the number of values in the set is odd) of the data is: 25. Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (b) What is the mode of the data? Comment on the data's modality (i.e., bimodal, trimodal, etc.). • This data set has two values that occur with the same highest frequency and is, therefore, bimodal. • The modes (values occurring with the greatest frequency) of the data are 25 and 35. Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (c) What is the midrange of the data? • The midrange (average of the largest and smallest values in the data set) of the data is: (70+13)=2 = 41.5 Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (d) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data? • The first quartile (corresponding to the 25th percentile) of the data is: 20. The third quartile (corresponding to the 75th percentile) of the data is: 35. Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (e) Give the five-number summary of the data. • The five number summary of a distribution consists of the minimum value, first quartile, median value, • third quartile, and maximum value. It provides a good summary of the shape of the distribution and for this data is: 13, 20, 25, 35, 70. Q3 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45,46, 52, 70. (f) Show a boxplot of the data. Q4 4) Suppose a manager tested the age and body fat data for 18 randomly selected adults with the following result 23 23 27 27 39 41 47 49 50 52 54 54 56 57 58 58 60 61 9.5 26.5 7.8 17.8 31.4 25.9 27.4 27.2 31.2 34.6 42.5 28.8 33.4 30.2 34.1 32.9 41.2 35.7 Q4 (a) Calculate the mean, median and standard deviation of age and score. • For the variable age the mean is 46.44, the median is 51, and the standard deviation is 12.85. • For the variable score the mean is 28.78, the median is 30.7, and the standard deviation is 8.99 Q4 (b) Draw the box-plots for age and score. 7.8 9.5 17.8 25.9 26.5 27.2 27.4 28.8 30.2 31.2 31.4 32.9 33.4 34.1 34.6 35.7 41.2 42.5 Q4 (b) Draw the box-plots for age and score. 23 23 27 27 39 41 47 49 50 52 54 54 56 57 58 58 60 61 Q4 (c) Draw a scatter plot and a q-q plot based on these two variables. Q4 (c) Draw a scatter plot based on these two variables. 23 23 27 27 39 41 47 49 50 52 54 54 56 57 58 58 60 61 9.5 26.5 7.8 17.8 31.4 25.9 27.4 27.2 31.2 34.6 42.5 28.8 33.4 30.2 34.1 32.9 41.2 35.7 Q4 (c) q-q plot based on these two variables. 23 23 27 27 39 41 47 49 50 52 54 54 56 57 58 58 60 61 7.8 9.5 17.8 25.9 26.5 27.2 27.4 28.8 30.2 31.2 31.4 32.9 33.4 34.1 34.6 35.7 41.2 42.5 Q5 Given two objects represented by the tuples (22, 1, 42, 10) and (20, 0, 36, 8): • (a) Compute the Euclidean distance between the two objects. • (b) Compute the Manhattan distance between the two objects. • (c) Compute the Minkowski distance between the two objects, using h = 3. • Q5 • To compute distance between Numeric attributes • Euclidean distance • The Manhattan (or city block) distance = Q5 • (22, 1, 42, 10) and (20, 0, 36, 8): (a) Compute the Euclidean distance between the two objects. = = =6.7082 Q5 • (22, 1, 42, 10) and (20, 0, 36, 8): (b) Compute the Manhattan distance between the two objects = = 11 Q5 • (22, 1, 42, 10) and (20, 0, 36, 8): (c) Compute the Minkowski distance between the two objects, using h = 3 = 6.1534