Statistics and Probability

Statistics and probability are two mathematical terms that analyze the frequencies of any event. We generally predict the outcome of many cases or the likelihood of a particular consequence. We often determine the result of events by calculating their probability. Tossing a coin, for instance, has two possible outcomes: head or tail. There is no way to forecast the outcome of such events with certainty, but they can be estimated based on probabilities. Statistics, on the other hand, deals with the collection, analysis, interpretation, organization, and presentation of the collected data. This data collection and presentation is crucial in almost every field. Whether it is a work meeting or an art exhibition, we need to organize the data. A well-organized data set facilitates better data management and understanding. 

Data representation in statistics 

Statisticians work with data. Data can be quantitative (numerical information) or qualitative (descriptive information). 

There are various ways of representing data. These are as follows:

• Frequency distribution table: A frequency distribution table is the arrangement of data in either ascending or descending order along with their frequencies.
• Bar graph: In a bar graph, the data appears in rectangular boxes concerning the x-axis and y-axis on graph paper. It is an easy to plot and widely used method. 
• Pie chart: In a pie chart, we divide a circle with different events, along with their proportions. To simplify, we can say that a pie chart is a circle with divisions based on the percentage of all events. 
• Line graph: A line graph shows data as dots connected by straight lines. 
• Pictograph: A pictograph is the representation of data in the form of pictures. 
• Histogram: In a histogram, we draw joint rectangles for representing the data on graph paper.

Measures of Central Tendency in Statistics

Central tendency is the representative value of any data in a specific order and format. Through it, we can easily comprehend large volumes of data. There are different methods for the determination of data in central tendency. These are as follows:

• Arithmetic mean: The arithmetic mean or simply the mean is the figure obtained by dividing the sum of all values of the given data by the number of values. 

x=∑x/n

where, x= mean, 

∑x= sum of all observations

n= number of observations.

• Median: Raw data is sorted ascendingly or descendingly for calculating the median. It is the value of the middle item based on the arrangement.  

Median (for odd number) = n+1/2

Median (for even number) = ½ [n/2th term + (n/2+1)th term]

• Mode: Mode is the highest or most common items of a given data. 

Mode= Item with the highest frequency

Formula for Probability

P (A) = number of favourable outcomes of an event total number of events occurring 

Types of Probability

Based on the nature of the outcome/results, there are four types of probability. These are as follows:

1. Classical probability: It is the total number of favourable outcomes of an event.
2. Empirical or experimental probability: It is the proportion of successful experiments divided by the number of trials.
3. Subjective probability: An individual’s own belief about the likelihood of an event is subjective probability. For example, while watching a cricket match, you often do the probability of winning of a particular team with your prospective.
4. Axiomatic probability: Axiomatic Probability has three rules for determining it. These are as follows:

• Any event shall have probability either greater than or equal to zero.
• Any predictable event will have probability, i.e. 1.
• Two mutually exclusive events will not coincide. However, the union states that only one of these events does occur.

An Example of probability

There is a bag with six brown coins and eight green coins. Let’s calculate the probability of randomly picking a blue coin. 

Solution:

To find the probability of brown coin, we shall assume it as P(B)

So, the number of favourable outcomes to get a brown coin is= 6

Total number of coins in the bag= 14

According to the formula of probability;

P(B)= number of favourable outcomes of an event /total number of events occurring 

=6/14

=3/7

Answer: The probability of getting a brown coin will be every 3 by 7.

Conclusion

Probability is the number of possible outcomes of a certain event, whereas statistics is the collection, analysis, and presentation of data or any event. In mathematics, both statistics and probability are powerful tools for analyzing events and data. Not only in mathematics, but almost all sectors use these techniques for presenting data. There are different methods of representing data in statistics such as bar graph, histogram, line graph, pictograph etc. The methods of measures of central tendency of data are mean, median, and mode. On the other hand, the method of finding probability is the ratio of the number of favourable outcomes to the total number of scenarios. Thus, explore these study material notes on statistics and probability.