Chapter 2Tutorial

2nd & 3rd LAB

Boxplot Example 1 11356678

121315

Draw the boxplot For the following set

Min=Q1=Median=Q3=Max=

IQR=1.5×IQR=Q1- 1.5×IQR=Q2+1.5×IQR=

Boxplot Example 1 11356678

121315

Draw the boxplot For the following set

Min=1Q1=3Median=6Q3=12Max=15

IQR=12-3=91.5×IQR=13.5Q1- 1.5×IQR=-10.5Q3+1.5×IQR=25.5

Boxplot Example 1

Sample 10

2

4

6

8

10

12

14

Min=1Q1=3Median=6Q3=12Max=15

Boxplot Example 2 23367779

131530

Draw the boxplot For the following set

Min=Q1=Median=Q3=Max=

IQR=1.5×IQR=Q1- 1.5×IQR=Q2+1.5×IQR=

Boxplot Example 2 23367779

131530

Draw the boxplot For the following set

Min=2Q1=3Median=7Q3=13Max=30

IQR=101.5×IQR=15Q1- 1.5×IQR=-12Q2+1.5×IQR=28

Boxplot Example 2

Sample 10

5

10

15

20

25

30

35

Min Outlier Max Outlier

Min=2Q1=3Median=7Q3=13Max=30

Q1- 1.5×IQR=-12Q2+1.5×IQR=28

Boxplot Example 2

Sample 10

5

10

15

20

25

30

35

Min Outlier Max Outlier

Min=2Q1=3Median=7Q3=13Max=30

Q1- 1.5×IQR=-12Q2+1.5×IQR=28

Terminate whiskers at the most extreme observation within 1.5×IQR of the quartiles

Q22) 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(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

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Q2(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.

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Q2(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

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Q2(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.

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Q2(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

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Q2(f) Show a boxplot of the data.

4, 5, 9, 11, 12, 13, 13, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20

Sample 10

2

4

6

8

10

12

14

16

18

Min Outlier Max Outlier

Q33) 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

(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.

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

(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.

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

(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

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

(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.

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

(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.

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

(f) Show a boxplot of the data.

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.

Q44) Suppose a manager tested the age and body fat

data for 18 randomly selected adults with the following result

23 9.523 26.527 7.827 17.839 31.441 25.947 27.449 27.250 31.252 34.654 42.554 28.856 33.457 30.258 34.158 32.960 41.261 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.

7.89.5

17.825.926.527.227.428.830.231.231.432.933.434.134.635.741.242.5

Q4(b) Draw the box-plots for age and score.

232327273941474950525454565758586061

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 9.523 26.527 7.827 17.839 31.441 25.947 27.449 27.250 31.252 34.654 42.554 28.856 33.457 30.258 34.158 32.960 41.261 35.7

Q4(c) q-q plot based on these two variables.

23 7.823 9.527 17.827 25.939 26.541 27.247 27.449 28.850 30.252 31.254 31.454 32.956 33.457 34.158 34.658 35.760 41.261 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