June 02, 2007
Basic Statistics
When people hear the word 'statitics' they usually react the same way when they hear 'mathematics', maybe even more than. Students want to distance themselves away from it as much as possible. I got a few pointers that can help you establish your understanding in basic statistics.
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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