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S1 Coding
Using coding to make numbers
easier to work with when data
values are large
Mean and Standard Deviation
Calculate the mean and standard deviation of
the following data set
3,10,15,7,8
Add 3 to each of the numbers and recalculate
the mean and standard deviation
Subtract 2 from each of the numbers and
recalculate the mean and standard deviation
Multiply each of the numbers by 10 and
recalculate the mean and standard deviation
Divide each of the numbers by 2 and
recalculate the mean and standard deviation
Solutions
Mean
Standard Deviation
x
x+3
x-2
10x
x/2
3
6
1
30
1.5
10
13
8
100
5
15
18
13
150
7.5
7
10
5
70
3.5
8
11
6
80
4
8.6
11.6
6.6
86.0
4.3
4.39
4.39
4.39
43.93
2.20
What do you notice about the coded results
compared to the original results?
Why does this happen?
x+a
Mean +a, standard deviation does not change
x-a
Mean - a, standard deviation does not change
ax
Mean x a, standard deviation x a
x/a
Mean/a, standard deviation /a
Example 1
A data set has been coded using y=x/10.
The standard deviation is 1.41
Find the standard deviation of the original data.
1.41 x 10 = 14.1
Example 2
A data set has been coded using y=x-20.
The standard deviation is 3.641
Find the standard deviation of the original data.
3.641 as the standard deviation does not change
Example 3
A data set has been coded using
y=x+100.
2
The standard deviation is 12.342
Find the standard deviation of the original data.
24.684
Adding 100 has no effect but the division by 2
has halved the standard deviation
E.G. 4 Time taken to complete reading a paper
Time take
(secs)
Freq
(f)
Midpoint
(x)
Coding
Y=x-500
1000
fy
fy²
0-3000
4
1500
1
4
4
3000-6000
16
4500
4
64
256
6000-8000
8
7000
6.5
52
338
8000-13000
2
10500
10
20
200
Σf=30
σ²
Σfy=140
Σfy² =798
=798 – 140 ² = 4.82
30
30
Coded σ
=2.19596
Original σ
=2195.96