Suppose that the data for analysis include the attribute age. The age values for the data tuples are (in increasing order) : 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. Use smoothing by bin means to smooth the above data, using a bin depth of 3. Illustrate your steps. Comment on the effect of this technique on the given data.

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Solution:

The following steps are required to smooth the above data using smoothing by bin means with a bin depth of 3.


Step 1:

Sort the data. (This step is not required here as the data are already sorted.)


Step 2:

Partition the data into equi-depth bins of depth 3.

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


Step 3:

Calculate the arithmetic mean of each bin.


Step 4:

Replace each of the values in each bin with the arithmetic mean calculated for the bin.

Bin 1: 142/3, 142/3, 142/3

Bin 2: 181/3, 181/3, 181/3

Bin 3: 21, 21, 21

Bin 4: 24, 24, 24

Bin 5: 262/3, 262/3, 262/3

Bin 6: 332/3, 332/3, 332/3

Bin 7: 35, 35, 35

Bin 8: 401/3, 401/3, 401/3

Bin 9: 56, 56, 56

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