applied maths

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17 Terms

1
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mutually exclusive rule

P(A) + P(B) = P(A∪B), P(A∩B) = 0

2
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Generalised addition law

P(A∪B) = P(A) + P(B) - P(A∩B)

3
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Independent events

P(A∩B) = P(A) x P(B)

4
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Binomial conditions

  • fixed number of trials

  • event is a success or a fail

  • constant probability of success

  • trials are independant

5
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binomial notation

X ~ B(n,p)

6
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Poisson conditions

  • singly in space or time (e.g telephone calls in an hour)

  • at random

  • independently

  • at a constant rate - the mean number of occurrences in the interval is proportional to the length of the interval

7
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opportunity sampling

take a sample from members of the population you have access to until you have a sample of desired size

advantages: doesn’t require size of population

disadvantages: unrepresentative

8
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systematic sampling

divide population by sample size then go up by this number

advantages: easy to select

disadvantages: less random, predetermined

9
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random sampling

generate sets of numbers, number the population, pick numbers ignoring repeats and numbers outside the region

advantages: equal chance

disadvantages: requires a list

10
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stratified sampling

proportional to the size of group: sample size/population x group size

advantages: fairly representative

disadvantages: requires a list

11
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outliers formula

lowest outlier:

Q1 - 1.5 x IQR

biggest outlier:

Q3 + 1.5 x IQR

12
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standard deviation

  • find the mean of the numbers

  • take the mean away from each number

  • square new column

  • total up new column and divide by how many numbers there are

  • square root to get the standard deviation (without square rooting you get the variance instead of standard deviation)

<ul><li><p>find the mean of the numbers</p></li><li><p>take the mean away from each number</p></li><li><p>square new column</p></li><li><p>total up new column and divide by how many numbers there are</p></li><li><p>square root to get the standard deviation (without square rooting you get the variance instead of standard deviation)</p></li></ul><p></p>
13
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standard deviation using frequency

  • Σf = the sum of the frequency column

  • Σfx² = f x x² or fx x x² added up

  • takeaway the mean²

  • square root

<ul><li><p><span>Σf = the sum of the frequency column</span></p></li><li><p><span>Σfx² = f x x² or fx x x² added up</span></p></li><li><p><span>takeaway the mean² </span></p></li><li><p><span>square root</span></p></li></ul><p></p>
14
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correlation

  • correlation does not imply causation

  • 1 = perfect positive, 0 = no correlation, -1 = perfect negative

15
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regression lines

  • interpolation - generally reliable if variables show a strong correlation

  • extrapolation - not reliable as there is not evidence that the pattern continues beyond the observed range

16
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interpreting gradient

as the (x variable) increases by 1 (unit) the (y variable) (increases/decreases) by (gradient) on average

17
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interpreting y intercept

it suggests the (y variable) will be (y intercept) when the (x variable) is 0