# S1 - MEI AS level notes

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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 of central tendancy
i.e. averages etc.
"sigma" means "the sum of..."
x
Mean =
n = x
Median = ( n2
+1
) th value
Mode = most common value
Midrange = (highest value+2lowest value )
Frequency Tables

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(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
Use midpoint as X
o Only gives estimated mean as exact data isn't used

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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 = X 2 - nX 2
2 2
X 2-nX (X -X )
n or
Mean Square Deviation {m.s.d}= Sxx
n or
n
Root Mean Square Deviation {r.m.s.d} =
Sxx

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Outlier
If a value is more than 2 standard deviations from mean you would investigate why it
was an outlier
Linear Coding
Coding is a method of simplifying calculations. It can also be used to convert units.
Example
Height x f xf
158.5 0 4 0
160.5 1 11 11
162.5 2 19 38
164.5 3 8 24
166.5 4 5 20
168.5 5 3 15
50 108
xf
x=
n
= 108
50 = 2.16cm
We can simplify the calculations by subtracting 158.…read more

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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 draw them so the AREA of
them are in proportion to their overall totals.…read more

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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 median of all values above the overall median
Even number of values:
Split the data into 2 halves and find the median of each half
I nterquartile Range = Q3 - Q1
Outliers

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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
EXHAUSTIVE events cover all possibilities
Estimated Probability
P (U ) = nn((U
T)
)
Number of times "u" happened
_ Total number of experiments
Probability of event "U"
Theoretical Probability
P (A) =Outcomes that give…read more

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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. The same flavour
b. Different flavours
a. Same Flavour
= P (S&V , S&V ) + P (SB, SB)
= 12 2
30 + 30
7
= 15

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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 the probability of something happening, given that another event has already
happened.
P (A|B) Means the probability of event A happening given that event B has already happened.…read more

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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 take certain values and are usually
best represented as a vertical line chart.
e.g. number of people in a car
Discrete random variables are often denoted by X.…read more