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Statistics
Chapter 1: Exploring Data
Distribution Shapes




Normal Distribution Uniform Distribution Bimodal
Unimodal No mode
Symmetrical
Non symmetrical distribution is SKEWED




Positive Skew Negative Skew
Variables
Discrete
o Can only take particular values {e.g. family size or shoe size etc}
Continuous
o Can take any value in a range
Measure…

Page 2

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Page 21 and 30
(X) No. of people in care Frequency (f)
1 13
2 20
3 7
4 4
Total 44


M edian = (44+1
2 ) th value
= 22.5th value = 2


fx
Mean =
n (n = f )

= 13+(2×20)+(3×7)+(4×4)
44

=2.045 =2
Grouped Tables…

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This is rarely used as the modulus function is hard to manipulate algebraically!
A better alternative is the SUM OF SQUARES or Sxx
Instead of using modulus, you square the difference to remove the negatives
2
Sxx = ( X - X ) This can be rearranged to




Sxx =…

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68% of data lies within 1 s.d. of the mean
95%of data lies within 2 s.d. of the mean
99.75% of data lies within 3 of the mean
Outlier
If a value is more than 2 standard deviations from mean you would investigate why it
was an outlier




Linear Coding…

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Chapter 2: Data Presentation
Bar Charts

Equal width bars
Gaps between bars
Height shows frequency
Usually for categorical (qualitative) data



Vertical Line Chart
Usually used for discrete data
Can only take fixed values (e.g. shoe size)



Pie Charts
Often if you have 2 pie charts comparing different totals you can…

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Quartiles
The lover quartile, median and upper quartile are denoted by Q1,Q2, Q3
For small data sets
th
M edian = (n+1
2 ) V alue (Where raw data is known)
Odd number of values:
Lower Quartile
Find the median of all values below overall median
Upper Quartile
Find the…

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Chapter 3: Probability
Notation
In stats an experiment is known as a TRIAL
An OUTCOME is any result you could get
An EVENT is a set of outcomes that follow a rule
Probability sum to 1 when mutually exclusive and exhaustive
MUTUALLY EXCLUSIVE events can't happen at the same time…

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Probability of Events from 2 Trials
Often we use tree diagrams. If there are more than 2 trials its usually not practical.
Example
Thomas buys a multipack of crisps. There are 2 smoky bacon and 4 salt & vinegar.
What is the probability that the first 2 picked are:
a.…

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"Either event A or event B"
P (AuB) = P (A) + P (B) For MUTUALLY EXCLUSIVE

A B = P (AuB)

= P (A) NOT Mutually Exclusive

= P (B)




P (AuB) = P (A) + P (B) - P (AnB) For NOT Mutually Exclusive
Conditional Probability
This is…

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X + Y = 20%

Y + Z = 10%

X + Y + Z = 25%

Y = 5%

Find the probability that someone has a hot breakfast and a hot lunch
P (HlnHb) = 5%




Chapter 4: Discrete Random Variables
Discrete random variables are variables which can only…

Comments

lLauren

can you explain to me why in chapter seven hypothesis tasting, that you say that P(X>8) = P(X=8)

Ben Williams

These were very helpful, however I did find a couple of errors. For example you have done the positive and negative skew the wrong way round. 

cathum

Sums up 190 pages into 16 pages. Sheer brilliance. /Virtual Claps 

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