Question

2. Use the methods below to normalize the following group of data: 150, 800, 640, 290, 2800

(a)min-max normalization by setting min = 0 and max = 1

(b) z-score normalization

(c) normalization by decimal scaling

Answer 1

Q.2) Given data as follows: 150, 800, 640, 290, 2800

minimum value = 150 and maximum value = 2800

a) min-max normalization by setting min = 0 and max = 1

Normalization for 150 is,

V' =[ ( 150 - 150) / (2800 - 150) ] * ( 1 - 0) + 0 = 0

Noralization for 800 is,

V' =[(800 - 150)/(2800 - 150) ] * (1 - 0) + 0 = 650/2650 = 0.2453

Similary we get for remaining data values,

Original Data	150	800	640	290	2800
[0,1] Normalized	0	0.2453	0.1849	0.0528	1

b) z-score normalization

From given data, sample mean = 936 and population standard deviation = 960.8038

z-score is,

z-score for 150 is,

Similary we get z-scores for remaining data values,

Original Data	150	800	640	290	2800
Z-score	-0.82	-0.14	-0.31	-0.67	1.94

c) Normalization by decimal scaling

For 150

V' = 150/10³ = 150/1000 = 0.15

Similarly we get, nirmalization by decimal scaling for remaining data values,

Original Data	150	800	640	290	2800
Decimal Scaling	0.15	0.80	0.64	0.29	0.28