Probability & Frequency of Distribution
PROBABILITY & FREQUENCY OF DISTRIBUTION
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Introduction
· Probability is
the measure of how likely a event will occur.
· A number that
express the ratio of favorable cases to the whole number of cases possible.
· For an example,
the chances of a coin landing on heads is 50% because a coin has two sides, so
there is 50% chance that the coin will land on tails and 50% that a coin will
land on heads.
· Probability of event to happen P(E) = Number of favorable outcomes/
Sample Question to
Calculate the Probability
Situation: - There is a container full of coloured bottles, red, blue, green and
orange. Some of the bottles are picked out and displaced. Sumit did this 1000
times and got the following results
- No. of blue bottles picked out: 300
- No. of red bottles: 200
- No. of green bottles: 450
- No. of orange bottles: 50
a)
What is the
probability that Sumit will pick a green bottle?
Ans: For every 1000 bottles picked out, 450 are green.
Therefore, P(green) = 450/1000 = 0.45
b)
If there
are 100 bottles in the container, how many of them are likely to be green?
Ans: The
experiment implies that 450 out of 1000 bottles are green.
Therefore, out of 100 bottles, 45
are green.
Application of Probability
· Risk Assessment
· Gambling
· Trading Decisions
· Entitlement
Analysis
· Financial
Regulations
· Pricing
· Insurance sector
Video description
Frequency of Distribution
Introduction
· Frequency of
distribution is a table that displays the frequency of various outcomes in a
sample.
· It shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class.
To represent the frequency of distribution some of the graphs can be used like
§ Histogram
§ Line charts
§ Bar charts
§ Pie charts
Types
1) Relative frequency distribution
·
Where each of the class frequencies is divided by the total number of
observations
2) Cumulative frequency distribution
·
Sum of the class and all classes below it in a frequency distribution
·
In simple words, you are adding up a value and all of the values that
came before it.
Sample Question to
Calculate the Frequency of Distribution
Example: A survey was taken on Maple Avenue. In each
of 20 homes, people were asked how many cars were registered to their
households. The results were recorded as follows:
3, 1, 4, 0, 2, 1, 5, 2, 1, 5, 4, 2, 3, 2, 0, 2, 1,
0, 3, 2.
Present this data in Frequency Distribution Table.
Also, find the maximum number of cars registered by
household.
Solution: Divide the
number of cars (x) into
intervals, and then count the number of results in each interval (frequency).
Thus
creating the frequency Distribution Table
|
Number of Cars |
Frequency |
|
0 |
3 |
|
1 |
4 |
|
2 |
6 |
|
3 |
3 |
|
4 |
2 |
|
5 |
2 |
Thus, from the table, it is clear that the 6 household has 2 cars.
Video description
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