Question

Exercise 2.2 gave the following data (in increasing order) for the attribute age: 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) Use smoothing by bin means to smooth these data, using a bin depth of 3. Illustrate your steps. Comment on the effect of this technique for the given data. (b) How might you determine outliers in the data? (c) What other methods are there for data smoothing?

Answer 1

Answer:

Step-by-step explanation:

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) Smoothing by bin means

Each bin has depth of 3

Dividing data into bins

so, Bin 1= 13, 15, 16

Bin 2=  16, 19, 20

Bin 3=  20, 21, 22

Bin 4= 22, 25, 25

Bin 5= 25, 25, 30

Bin 6= 33, 33, 35

Bin 7 = 35, 35, 35

Bin 8= 36, 40, 45

Bin 9=  46, 52, 70

Now, smoothing data by bin mean

so, Bin 1= 13, 15, 16 = (13+15+16)/3 = 15 Bin 1 = 15,15,15

Bin 2=  16, 19, 20 = (16+19+20)/3 = 18 Bin 2 = 18,18,18

Bin 3=  20, 21, 22= (20+21+22)/3 = 21 Bin 3 = 21,21,21

Bin 4= 22, 25, 25 = (22+25+25)/3 = 24 Bin 4 = 24,24,24

Bin 5= 25, 25, 30 =(25+25+30)/3 = 27 Bin 5 = 27,27,27

Bin 6= 33, 33, 35 = (33+33+35)/3 = 34 Bin 6 = 34,34,34

Bin 7 = 35, 35, 35 = (35+35+35)/3 = 35 Bin 7 = 35,35,35

Bin 8= 36, 40, 45 = (36+40+45)/3 = 40 Bin 8 = 40,40,40

Bin 9=  46, 52, 70=(46+52+70)/3 = 56 Bin 9 = 56,56,56

This technique is used to smooth the data. Data may have noise, using binning techniques we can remove noise from the data. It helps in providing more accurate results

b) How might you determine outliers in the data?

Outliers are the data that are abnormal to other data points. Outliers can be found by Box and whisker chart (box plot). Inter Quartile range can also be used to identify outliers

c)  What other methods are there for data smoothing?

Other methods of smoothing data are

a) binning by boundaries

b) Exponential smoothing

c) Random walk