Business Statistics Flashcards
Q1=
0.25 (n+1)th value
Q3=
0.75 (n+1)th value
Ecart entre 2 quartiles =
Interquartile range
Median =
To find the Median, place the numbers in value order and find the middle.
Median in a grouped data =
Find the Inter-quartile range in Grouped Data
Use the same formula as the median but divide the total per 4 for Q1 or multiply per 3/4 for Q3
Coefficient of variation (CV)=
Measure of relative dispersion
s=𝞼= standard deviation
ẍ=𝞵=mean
Measure of Skewness
Standard deviation =
s or 𝞼
square root of variance
√𝞼2
Variance =
𝞼2
Average of squared differences from the mean
When should we prefer the mean or the median ?
The mean is mostly preferred because it uses all the data values
However, in case of extreme values, the median might be more representative
Sample variance formula
How to estimate the mean of grouped data ?
We can estimate the Mean by using the midpoints.
The complement of an event is ..
Everything in the sample space apart from that event.
P(Ā)=P(Ac)=1−P(A)
The Addition Rule =
(A union B)
P(A or B) = P(A∪B) = P(A) + P(B) - P(A∩B)
If A and B are mutually exclusive: P(A∩B) =0
The Multiplication Rule
(A inter B)
P(AandB)=P(A∩B)=P(A)*P(B)
If A and B are mutually exclusive: P(A∩B) =0
Conditional Probability
(P de A sachant B)
If A and B are independent, then:
P(A | B)= P(A) and P(B | A) = P(B)
P(A ∩ B) = P(A) * P(B)
How can we establish the number of ways of having 3 girls and 2 boys?
Combinations (order is not important):
What does the ! mean ?
It is all the numbers multiplied together before it.
So if you put 3!, it gives 1x2x3=6
Or if you put 6! it gives
Bayes’ Theorem :
General Bayes’ Theorem
What is Decision Analysis ?
Analysis of decision making where risk is involved
Mean of a Discrete Random Variable
μ=E(x)=∑xi Pr(xi)
Variance of a Discrete Random Variable =
σ2=Ε(x−μ)2=∑(xi−μ)2Pr(xi)
What is a Binomial Situation ?
Random situation, in which there are:
- n identical and independent trials;
- only two possible outcomes: success (with probability p) or failure (with probability 1-p);
- The probability of success remains the same between trials.
• The probability of x = r successes in n trials and probability of success at each trial equal to p is:
p(x=r)=nCr×pr×(1−p)n-r
nCr =
By definition, 0!=
1
The expected value (mean or expectation) of a Binomial random variable, r∼B(n,p), is:
μ = Ε(r)= np
The variance of a Binomial random variable, r∼B(n,p), is:
σ2 =np(1−p)
The Poisson Distribution
P(x) =
Where:
μ = mean of the distribution
x = number of occurrences
The Poisson Distribution
E(X)
Var(x)
Where:
μ = mean of the distribution
x = number of occurrences
The two parameters of the Normal distribution are….
The mean (μ) and the variance (σ2)
x ∼N(μ,σ2)
The Normal distribution with mean = 0 and variance = 1 is called the …
Standard Normal Distribution
The letter z (also known as z-score) is …
Usually used for random variables, which have been standardised, i.e., converted to new random variables with mean zero and variance (standard deviation) equal to one
Z ∼ N(0,1)
Use the A2 table to find Z when…
P(Z > a)
Continuity Correction
- The binomial distribution is a discrete distribution .
- The normal distribution is a continuous distribution.
- Accordingly, P(x = a) is approximated by P(a - 0.5 < x < a + 0.5).
- If we require P(x < a) for the Binomial we need P(x < a - 0.5) for the Normal
- If we require P(x > a) for the Binomial we need P(x > a + 0.5) for the Normal
95% Probability Interval Estimates :
Pr(μ-1.96√(σ2 /n) ≤ x ≤ μ+1.96√(σ2 /n))
