When you grasp thse basic ideas you will begin to see how variables affcet a population. From that you will then be able to easily appriciate all the next level operations and how they are arrived at.
Hope this hepls out...
A
| original population | orig x 10 | orig + 20 | (origx5)+30) | (org+30) x 5 |
| 0 | 0 | 20 | 30 | 150 |
| 1 | 10 | 21 | 35 | 155 |
| 1 | 10 | 21 | 35 | 155 |
| 3 | 30 | 23 | 45 | 165 |
| 3 | 30 | 23 | 45 | 165 |
| 3 | 30 | 23 | 45 | 165 |
| 4 | 40 | 24 | 50 | 170 |
| 6 | 60 | 26 | 60 | 180 |
| 6 | 60 | 26 | 60 | 180 |
| 7 | 70 | 27 | 65 | 185 |
| 10 | 100 | 30 | 80 | 200 |
sum | 44 | 440 | 264 | 550 | 1870 |
average | 4 | 40 | 24 | 50 | 170 |
stdv | 3 | 30 | 3 | 15 | 15 |
var | 9 | 900 | 9 | 225 | 225 |
range | 10 | 100 | 10 | 50 | 50 |
count | 11 | 11 | 11 | 11 | 11 |
median | 3 | 30 | 23 | 45 | 165 |
mode | 3 | 30 | 23 | 45 | 165 |
The table above was constructed based on how spacific variables affect a give population using the SPSS program. I think you already saw a trend or a pattern in each class of variables.
Below I explain how each class of variables affect the population. Check the derived formulae and place the in the population variables and see how they work.
:.It is seen.
| | | | | | |
{ set} x a | a(mean) | a(stdv) | a(var) | a(median) | a(mode) | a(range) |
{set + a } | (mean + a) | (stdv) | (var) | (median + a) | (mode + a) | (range) |
var & stdv are only affected by multiplication i.e. var_{new} = a^{2}(var_{old})
stdv_{new}= a(stdv_{old})
In case of combined operations i.e. ( {set+ b } x a)
Var & range is only affected by a as demonstrated in
A
mean_{new} = [a(mean_{old})] + b
median_{new} = [a(median_{old})] + b
mode_{new} = [a(mode_{old})] + b
3. In the case of another combined operation i.e. [(a{set}) + b]
Var and range are affected as in
A.
mean_{new} = a(mean_{old} +b)
median_{new }= a(median_{old} + b)]
mode_{new} = a(mode_{old}+ b)
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