DCA1206 BASIC STATISTICS AND PROBABILITY JULY SEPTEMBER 2025

Description

SESSION	JULY / SEPTEMBER 2025
PROGRAM	BACHELOR OF COMPUTER APPLICATIONS (BCA)
SEMESTER	2
COURSE CODE & NAME	DCA1206 BASIC STATISTICS AND PROBABILITY

 

 

Set – I

 

 

Q1. a. Define data and explain different types of data used in statistics. Give suitable examples from computer applications.   5         

1. Describe the steps involved in organizing and presenting data through frequency tables and diagrams. 5

Ans 1.

(a) Definition of Data and Types of Data Used in Statistics

Data

In statistics, data refers to a collection of facts, figures, observations, or values that are gathered for the purpose of analysis and decision-making. Data serves as the foundation of statistical study and helps in understanding patterns, trends, and relationships. In computer applications, data is generated continuously through software systems, databases, networks, and user interactions, making statistical analysis highly relevant.

Types of Data Used in Statistics

Statistical data is broadly classified based on its nature and characteristics.

Qualitative data: Qualitative data, also known as categorical data, represents non-numerical

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Q2. a. Explain the concept of a measure of central tendency. Why is it important in statistical analysis? 5   

1. Find the arithmetic mean and median for the following data: 10, 15, 20, 25, 30, 35, 40

Ans 2.

(a) Concept and Importance of Measures of Central Tendency

Meaning of Central Tendency

Measures of central tendency are statistical tools used to identify a single value that represents the center or typical value of a dataset. They summarize large sets of data into one representative figure, making interpretation easier.

The most common measures of central tendency are mean, median, and mode. Each measure provides a different perspective on the data distribution.

Importance in Statistical Analysis

Central tendency is important because it provides a quick understanding of data behavior. In

 

 

Q3.a. Define the term dispersion and explain its significance in comparing datasets.   

1. Calculate the range and standard deviation for the following values: 5, 10, 15, 20,

Ans 3.

1. Dispersion and Its Numerical Measurement

Dispersion

In statistics, dispersion refers to the degree to which individual data values are spread out or scattered around a central value such as the mean or median. While measures of central tendency provide a single representative value of a dataset, they do not reveal how closely or widely the data values are distributed around that central point. Dispersion fills this gap by explaining the extent of variability present in the data.

A dataset in which values are very close to each other is said to have low dispersion, whereas

 

 

Set – II

 

Q4. a. Explain the fundamental counting principle and its importance in probability calculations.     5         

1. What is a sample space? Distinguish between finite, infinite, discrete, and continuous sample spaces with examples. 5

Ans 4.

(a) Fundamental Counting Principle and Its Importance in Probability

Fundamental Counting Principle

The Fundamental Counting Principle is a basic rule used in probability and combinatorics to determine the total number of possible outcomes of an experiment that occurs in multiple stages. According to this principle, if one event can occur in m different ways and a second independent event can occur in n different ways, then the total number of ways both events can occur together is m × n. This principle can be extended to any number of stages.

The rule is based on logical reasoning rather than complex formulas and provides a

 

 

Q5. a. Differentiate between independent and dependent events with one example each.

1. Define mutually exclusive and exhaustive events. Explain how they affect the calculation of probability. 5

Ans 5.

(a) Independent and Dependent Events with Examples

Independent Events

Independent events are events in which the occurrence of one event does not influence or change the probability of occurrence of another event. In such cases, the outcome of one experiment has no effect on the outcome of the other experiment. Each event occurs on its own without any dependency.

For example, tossing a coin and rolling a die are independent events. If a coin is tossed and

 

 

Q6. a. State and explain the addition and multiplication rules of probability with suitable examples. 5         

1. What is conditional probability? Explain how Bayes’ Theorem helps in decision-making using a real-world example. 5

Ans 6.

(a) Addition and Multiplication Rules of Probability with Examples

Addition Rule of Probability

The addition rule of probability is used to calculate the probability that at least one of two events will occur. If two events are mutually exclusive, the probability of either event occurring is equal to the sum of their individual probabilities.

For example, when a die is rolled, the probability of getting either 2 or 5 is calculated by adding the probability of getting 2 and the probability of getting 5. This rule is widely used when events cannot happen simultaneously.