# Statistics - S1

Mind Map by Alessandra Genco, updated more than 1 year ago
 Created by Alessandra Genco almost 6 years ago
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### Description

Maths Mind Map on Statistics - S1, created by Alessandra Genco on 05/08/2014.

## Resource summary

Statistics - S1
1 Mathematical models in probability and statistics
1.1 A mathematical model is a simplification of a real world situation.
1.2 Advantages of mathematical models are they are quick and easy to produce, they can simplify a more complex situation, they can help us improve our understanding of the real world as certain variables can readily be changed, they enable predictions to be made about the future, they can help provide control.
1.3 Disadvantages of mathematical models are they only give a partial description of this real situation and they only work for a restricted range of values.
2 Representation and summary of data
2.1 CONTINUOUS VARIABLE - a variable that can take any value in a given range
2.1.1 Divide n by 2 and use interpolation to find the value of corresponding term
2.2 DISCRETE VARIABLE - is a variable that can take only specific values in a given range
2.2.1 Divide n by 2, if the answer is a whole number find the mid point, if not, round the number up
3 Measures of dispersion
3.1 To find there standard deviation, square root the variance
3.2 When you have coded data in order to find the uncoded answer you do the reverse, however for standard deviation only multiplication or division affects the answer not anything that has been added or subtracted, where as when calculating the original mean you have to do the opposite of both adding/subtracting and multiplication/division
4 Representation of data
4.1 OUTLIER is an extreme value. To find outliers use the calculation: 1.5 X IQR and subtract from lower and add onto upper quartile
4.2 To find the skew: 3(mean - median) divided by standard deviation, median < mean = positive, median > mean = negative Q2 - Q1 < Q3 - Q2 = positive, Q2 - Q1 > Q3 - Q2 = negative
5 Probabilty
5.1 A and B are independent if P(A n B) = P(A) X P(B)
5.2 A and B are mutually exclusive P(A n B = 0)
5.4 Conditional Probability
6 Correlation
6.1 The closer r is to 1, the closer it is to a positive linear correlation
6.2 r is never affected by coding
7 Regression
7.1 The sequence is y = a + bx
7.2 The regression of a coefficient
8 Discrete Random Variables
8.1 The sum of all the probabilities must add up to one ΣP (X=x) = 1
8.2 The expected value of X (mean) = ΣxP(X=x)
8.3 Variance of X (VarX) = Σx2 P(X=x) then minus the mean squared
8.4 For a discrete uniform distribution you can calculate the mean you do n + 1 divided by 2, and to calculate the variance you do (n+1) (n-1) divided by 12
9 Normal distribution
9.1 Z = X - mean / standard deviation

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