Business Statistics

Question 1

Q1=

Answer 1

0.25 (n+1)^th value

Question 2

Q3=

Answer 2

0.75 (n+1)^th value

Question 3

Ecart entre 2 quartiles =

Answer 3

Interquartile range

Question 4

Median =

Answer 4

To find the Median, place the numbers in value order and find the middle.

Question 5

Median in a grouped data =

Answer 5

Question 6

Find the Inter-quartile range in Grouped Data

Answer 6

Use the same formula as the median but divide the total per 4 for Q1 or multiply per 3/4 for Q3

Question 7

Coefficient of variation (CV)=

Answer 7

Measure of relative dispersion

s=𝞼= standard deviation

ẍ=𝞵=mean

Question 8

Measure of Skewness

Answer 8

Question 9

Standard deviation =

Answer 9

s or 𝞼

square root of variance

√𝞼²

Question 10

Variance =

Answer 10

𝞼²

Average of squared differences from the mean

Question 11

When should we prefer the mean or the median ?

Answer 11

The mean is mostly preferred because it uses all the data values

However, in case of extreme values, the median might be more representative

Question 12

Sample variance formula

Answer 12

Question 13

How to estimate the mean of grouped data ?

Answer 13

We can estimate the Mean by using the midpoints.

Question 14

The complement of an event is ..

Answer 14

Everything in the sample space apart from that event.

P(Ā)=P(A^c)=1−P(A)

Question 15

The Addition Rule =

(A union B)

Answer 15

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

Question 16

The Multiplication Rule

(A inter B)

Answer 16

P(AandB)=P(A∩B)=P(A)*P(B)

If A and B are mutually exclusive: P(A∩B) =0

Question 17

Conditional Probability

(P de A sachant B)

Answer 17

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)

Question 18

How can we establish the number of ways of having 3 girls and 2 boys?

Answer 18

Combinations (order is not important):

Question 19

What does the ! mean ?

Answer 19

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

Question 20

Bayes’ Theorem :

Answer 20

Question 21

General Bayes’ Theorem

Answer 21

Question 22

What is Decision Analysis ?

Answer 22

Analysis of decision making where risk is involved

Question 23

Mean of a Discrete Random Variable

Answer 23

μ=E(x)=∑x_i Pr(x_i)

Question 24

Variance of a Discrete Random Variable =

Answer 24

σ²=Ε(x−μ)²=∑(x_i−μ)²Pr(x_i)

Question 25

What is a Binomial Situation ?

Answer 25

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.

Question 26

• The probability of x = r successes in n trials and probability of success at each trial equal to p is:

Answer 26

p(x=r)=nCr×p^r×(1−p)^n-r

Question 27

nCr =

Answer 27

Question 28

By definition, 0!=

Answer 28

1

Question 29

The expected value (mean or expectation) of a Binomial random variable, r∼B(n,p), is:

Answer 29

μ = Ε(r)= np

Question 30

The variance of a Binomial random variable, r∼B(n,p), is:

Answer 30

σ² =np(1−p)

Question 31

The Poisson Distribution

P(x) =

Answer 31

Where:

μ = mean of the distribution

x = number of occurrences

Question 32

The Poisson Distribution

E(X)

Var(x)

Answer 32

Where:

μ = mean of the distribution

x = number of occurrences

Question 33

The two parameters of the Normal distribution are….

Answer 33

The mean (μ) and the variance (σ²)

x ∼N(μ,σ²)

Question 34

The Normal distribution with mean = 0 and variance = 1 is called the …

Answer 34

Standard Normal Distribution

Question 35

The letter z (also known as z-score) is …

Answer 35

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)

Question 36

Use the A2 table to find Z when…

Answer 36

P(Z > a)

Question 37

Continuity Correction

Answer 37

• 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).

1. If we require P(x < a) for the Binomial we need P(x < a - 0.5) for the Normal
2. If we require P(x > a) for the Binomial we need P(x > a + 0.5) for the Normal

Question 38

95% Probability Interval Estimates :

Answer 38

Pr(μ-1.96√(σ² /n) ≤ x ≤ μ+1.96√(σ² /n))