Attached.

Topic: Probability
a) (5 marks)

Describe the classical method determine probability with example.

Classical method of determining probability is based on the concept of a statistical
experiment in which the number of possible outcomes is discrete and each outcome is equally
likely. The probability of each outcome is therefore equal to 1 divided by total number of
outcomes. For example in a fair dice, for one toss, there are six possible outcomes; 1, 2, 3, 4, 5,
and 6.
The probability of each outcome =1/total number of outcomes = 1/6

With reference from the Table Summary Table below, discuss the meaning, interpretation and any
important implications of the following statistics in column B:
Passengers
(100,000s)
Descriptive statistics

B

Values are in (100,000s)

Mean (2 marks)

22.58333333 The mean gives the average of all values for a variable of
interest in a dataset. It is a measure of central tendency
and is an estimator of the expected average value of all
values in a dataset. For example, the mean of 22.583
indicates that the average number of passengers in the
dataset is equal to 22.5833

Standard Error
(2 marks)

2.805455544 The standard error is a measure of variation and
measures the expected accuracy in using the sample
mean as an estimator of population mean.

Median (2 marks)

22

The median is a measure of central tendency and gives
the central value dividing the upper 50% values by
quantity from the lower 50% values. It therefore gives the
central value around which all values of a variable of
interest in a dataset revolve around. For example, the
median value of 22 indicates that the central number of
passengers dividing the largest 50% of values from the
smallest 50% of values for number of passengers is 22
1

Mode (2 marks)

15

The mode gives the number that appears most in the
data set. The mode value is 15. The value indicates that
15 is the number that appears most for the number of
passengers.

Standard Deviation
(2 marks)

9.71838308

The standard deviation gives the average deviation of all
values from the average or mean value. The standard
deviation is 9.718 and indicates that individual passenger
values differ from the mean by an average of 9.7184

Sample Variance
(2 marks)

94.4469697

Variance measures how spread out values are from each
other. It gives the average of the squared distances from
each point to the mean. The value of 94.447 indicates
that values are highly spread out from each other.

Kurtosis
(3 marks)

0.723953163 Kurtosis is a measure of the distribution of a variable of
interest. It is a measure of the peakedness or flatness of a
distribution compared with the normal distribution. The
positive value of 0.7239 indicates that the distribution is
flatter as compared to a normal distribution.

Skewness
(3 marks)

0.899057655 Skewness is a measure of the distribution of a variable of
interest. It is a measure of how skewed data is as
compared to the normal distribution. The positive value
of 0.899 indicates that the distribution is positively
skewed as compared to a normal distribution.

2

Range (2 marks)

34

The range gives the difference between the largest and
smallest value for a variable of interest in a dataset. In
this case, the difference between the largest and smallest
value for the number of passengers is 34.

Minimum (1 marks)

10

Minimum gives the smallest value for a variable of
interest in a dataset. In this case the smallest number of
passengers is 10.

Maximum (1 marks)

44

Maximum gives the smallest value for a variable of
interest in a dataset. In this case the largest number of
passengers is 44.

Sum (2 marks)

271

Sum gives the total of all values for a variable of interest
in a dataset. In this case the total number of passengers is
271.

Count (2 marks)

12

Count gives the number of data points for a given variable
in a dataset. For the dataset, the number of data points in
the variable, number of passengers, is 12.

Question Three (26 marks)
(a) What are the purposes of regression analysis? How does it help business? Provide a clear
relevant example with an explanat...