IGNOU FREE BECS-184 Data Analysis Solved Guess Paper Questions 2025

Q1. Explain the meaning and scope of Statistics. What are its functions in data analysis?

Statistics is a discipline that deals with the collection, classification, presentation, analysis, and interpretation of numerical data. It helps convert raw data into meaningful information. The scope of statistics includes descriptive statistics (summarizing data) and inferential statistics (drawing conclusions about a population based on a sample). Descriptive statistics deals with measures like mean, median, mode, dispersion, and graphical representation. Inferential statistics uses sampling, hypothesis testing, confidence intervals, and regression analysis.

The major functions of statistics in data analysis include data collection, which involves selecting appropriate tools and techniques to gather information. Statistics also helps in data organization and presentation, such as tables, charts, and frequency distributions that make data understandable. Through techniques like averages and dispersion, statistics performs data summarization. Another function is data analysis, which interprets numerical patterns and relationships using tools like correlation, regression, and probability.

Statistics further supports decision-making by offering scientific methods to analyze trends, predict outcomes, and evaluate alternatives. In research, statistics ensures validity and reliability by guiding sampling procedures and measurement techniques. Overall, statistics makes complex data manageable and meaningful.

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Q2. What are the measures of central tendency? Explain mean, median, and mode.

Measures of central tendency are statistical tools used to determine the central or typical value of a dataset. They summarize the entire data with a single representative value. The three main measures are mean, median, and mode.

Mean is the arithmetic average of all observations. It is calculated by dividing the sum of all values by the number of observations. The mean is easy to compute and widely used, but it is affected by extreme values (outliers). For interval and ratio data, the mean provides a precise central value and is used in many statistical formulas, including variance and regression.

Median is the middle value when data are arranged in ascending or descending order. If the number of observations is odd, the median is the central value; if even, it is the average of the two central values. Median is a better measure than mean when the data are skewed or include outliers. It is often used for income distribution, real estate prices, and non-normal datasets.

Mode is the value that appears most frequently in a dataset. A dataset can be unimodal (one mode), bimodal (two modes), or multimodal. Mode is useful for categorical data where mean and median cannot be applied, such as finding the most preferred product or most common category. It is also used to understand the shape of a distribution.

Together, mean, median, and mode provide a comprehensive understanding of a dataset’s central behavior. Each measure has its strengths depending on the type and distribution of data.

Q3. Explain the concept of dispersion. Describe range, quartile deviation, and standard deviation.

Dispersion describes the spread or variability of data around a central value. While measures of central tendency show the center of data, dispersion reveals how scattered the values are. The main measures of dispersion include range, quartile deviation, and standard deviation.

Range is the simplest measure and is calculated as the difference between the maximum and minimum values. It gives a quick idea of the spread but is highly affected by extreme values. Range is useful for preliminary analysis but not reliable for detailed studies.

Quartile Deviation (QD) measures the spread of the middle 50% of the data. It is computed using the first (Q1) and third (Q3) quartiles:
QD = (Q3 – Q1) / 2
Since it ignores extreme values, it is more stable than range. QD is helpful in analyzing skewed distributions and datasets with outliers.

Standard Deviation (SD) is the most widely used measure of dispersion. It represents the average deviation of each observation from the mean. SD is calculated by taking the square root of the variance (average squared deviation from the mean). A low SD indicates that the data points cluster near the mean, while a high SD indicates wide variability. SD is essential in probability, hypothesis testing, regression, and many statistical models because it considers every value in the dataset.

Thus, measures of dispersion help understand data consistency, reliability, and variability. They complement central tendency measures to give a fuller picture of dataset characteristics.

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Q4. Describe different methods of data collection with examples.

Data collection refers to gathering information for analysis. It can be classified into primary and secondary data collection.

Primary data are collected directly from the source. Methods include:

1. Observation – Researchers observe behavior, events, or conditions. For example, observing customer movement in a retail store.

2. Interview – Direct questioning through personal, telephone, or online interviews. Useful for surveys and qualitative research.

3. Questionnaires – Written sets of questions distributed to respondents. They are cost-effective and suitable for large samples.

4. Experiments – Conducted under controlled conditions to test relationships, such as in scientific research.

Secondary data are collected from existing sources such as government reports, journals, websites, census data, and databases. These are inexpensive and readily available but may not always match specific research needs.

Q5. What are frequency distributions? Explain the types and uses.

A frequency distribution summarizes raw data into classes and shows how often each class occurs. It organizes large datasets into a readable format.

Types include:

1. Ungrouped frequency distribution – Data listed individually with their frequencies.

2. Grouped frequency distribution – Data arranged in class intervals (e.g., 0–10, 11–20).

3. Cumulative frequency distribution – Shows cumulative totals of frequencies.

4. Relative frequency distribution – Shows frequency as a percentage of total.

Frequency distributions help identify patterns, central values, and dispersion, and form the basis for histograms, ogives, and statistical analysis.

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Q6. Explain graphical presentation of data and discuss its types.

Graphical presentation converts numerical data into visual formats to enhance understanding. Common graphs include bar charts, pie charts, histograms, frequency polygons, and line graphs.

• Bar charts represent categorical data.

• Pie charts show percentage distribution.

• Histograms display continuous data.

• Line graphs show trends over time.

Graphs make complex data easy to interpret and help in pattern recognition, comparison, and decision-making.

Q7. What is correlation? Explain Karl Pearson’s correlation coefficient.

Correlation measures the relationship between two variables. It indicates whether an increase in one variable is associated with an increase or decrease in another.

Karl Pearson’s correlation coefficient (r) measures linear correlation. It ranges from –1 to +1.

• +1 means perfect positive correlation

• –1 means perfect negative correlation

• 0 means no linear correlation

Pearson’s r is calculated using covariance and standard deviations of variables. It is widely used in economics, business, and research.

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Q8. Explain regression analysis. How is it useful in forecasting?

Regression analysis studies the relationship between a dependent variable and one or more independent variables. Simple linear regression uses one independent variable to predict outcomes.

The regression equation is:
Y = a + bX
Where a = intercept, b = slope.

Regression helps forecast future values, identify trends, and understand cause-effect relationships.

Q9. What are index numbers? Explain their construction and uses.

Index numbers measure changes in economic variables over time, such as prices, wages, or production. Types include price index, quantity index, and value index.

Construction Steps:

1. Selection of base year

2. Selection of items

3. Collection of data

4. Choosing a formula (Laspeyres, Paasche, Fisher)

5. Calculation and interpretation

Index numbers help measure inflation, cost of living, and economic trends.

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Q10. What is qualitative data analysis? Explain methods like coding and thematic analysis.

Qualitative data analysis involves interpreting non-numerical data such as interviews, documents, and observations. Methods include:

Coding – Assigning labels to meaningful segments of data.
Thematic analysis – Identifying patterns or themes across data.
Content analysis – Systematic review of text to quantify patterns.

Qualitative analysis helps understand human behavior, experiences, and social processes.

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