About Probability and Statistics
What is Probability?
The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur. What are the chances of a coin landing on heads, for instance, when we toss the coin in the air? The number of outcomes that could occur is the basis for the response to this question. The outcome in this case might be either heads or tails. Therefore, there is a 50% chance that the result will be heads.
Probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. It can be expressed in the form of fractions, decimals or percents.
The Probability formula is as follows:
Describing Likelihood
What is Statistics?
The study of data gathering, analysis, interpretation, presentation, and organisation is known as statistics. It is a technique for gathering and analysing data. This has numerous uses on both a local and large scale. Statistics or ‘Stats’ are utilised in all forms of data research, whether it is for studying a nation’s population or its economy.
Numerous disciplines, including sociology, psychology, geology, and weather prediction, have a necessity for statistics. Here, both quantitative and qualitative data are being gathered for analysis. Discrete and continuous quantitative data are just two examples of the two forms available. While continuous data does not have a fixed value but instead has a range, discrete data has a fixed value. In this notion, numerous words and formulas are utilised.
Rapid Recall
Solved Examples
Example 1: You have been given a frequency distribution table, consisting of the weights of 35 students of a class:
Weights (in kg) | Number of students |
|---|---|
31 – 35 | 10 |
36 – 40 | 4 |
41 – 45 | 15 |
46 – 50 | 2 |
51 – 55 | 1 |
56 – 60 | 2 |
61 – 65 | 2 |
66 – 70 | 1 |
71 – 75 | 1 |
(i) Note down the class-interval for classes 41 – 45?
(ii) write the number of students in the range of 56 – 60 kgs?
Solution:
(i) Class interval = Upper class limit – lower class limit
= 45 – 41
= 4
(ii)The number of students in the range 56-60 kgs is 2.
Example 2: Steph and Rony are two players in an intense game of tennis . The probability of Steph’s victory is 0.73. What is the probability that Rony will win the match?
Solution:
Let S denote the event where Steph wins the match and R denote the event where Rony wins the match.
The probability of Steph to win = P(S) = 0.73
The probability of Rony to win = P(R) = 1 – P(S)
= 1 – 0.73 = 0.27
Therefore , the probability of Rony winning the match is 0.27.
Observing the population of our country in the last two decades, which has been steadily increasing.
Keeping a track of the number of chairs and tables in a classroom.
While statistics examines the frequency of events in the past, probability deals with estimating the possibility of future events.
The study of the effects of mathematical definitions is the main focus of the theoretical area of mathematics known as probability. In its core, statistics is a field of mathematics that seeks to explain observations in the real world.
The sum of all observations divided by the total number of observations yields the arithmetic mean of a set of data.
The median of the data is the value of the middle observation after the data have been arranged in either ascending or descending order.
A data mode is the value that appears the most frequently in the provided data, or the observation with the highest frequency.