**1.) Discuss an overview of Statistics.**

**ans:** **Business Statistics** is defined as the systematic practice of collecting, analyzing, interpreting, and presenting data, relevant to business operations and decision-making.

**2.) What are the use of statistics in business?**

**ans:** The use of statistics in business are as follows:

- Market Research
- Financial Analysis
- Operations Management
- Sales Forecasting
- Supply Chain Management

**3.) Describe basic vocabulary of statistics.**

**ans:** The seven basic vocabulary terms of statistics are:

**Variable:**

A characteristics of an item that can differ from one individual to the next and will be analyzed using statistics is called variable.

**Data:**

The different values associated with a variable is called data. In the context of statistics, data can take various forms, such as numbers, measurements, or categorical observations. It serves as the raw material for statistical analysis.

**Operational Definition:**

An operational definition defines a concept or term in terms of the specific operations or procedures used to measure or observe it.

â€¢ It provides a clear and unambiguous description of how a variable is measured or manipulated, ensuring consistency in research and experimentation.

**Population**:

Population is a collection of all the items or individual under statistical investigation about which we are trying to draw some conclusion.

**Sample**:

A small representative portion of the population selected for analysis is called sample.

â€¢ It is chosen to represent the larger population, and the goal is to draw conclusions about the population based on the analysis of the sample.

**Parameter:**

A parameter is a numerical value that describes some characteristics of a population. **For example**, the population mean, standard deviation, or proportion are parameters.

**Statistics:**

**Statistics **is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

**4.) What is a variable? Explain types of variable.**

**ans:** A characteristics of an item that can differ from one individual to the next and will be analyzed using statistics is called variable.

**5.) Describe the scale of management.**

**ans:**

**6.) Define classification and various method of classification.**

**ans:** The various method of classification are:

**7.) Discuss the problem in the construction of a frequency distribution from raw data with particular reference to the choice of number of classes and class limits.**

**ans:**

**8.) What points should be taken into consideration for constructing a grouped frequency distribution.**

**ans:** The points should be taken into consideration for constructing a grouped frequency distribution are:

- Number of classes
- Class width or size of the class intervals
- Class limits
- Some other consideration like: open end classes.

**9.) Explain, in brief, the basic principles and rules for forming a grouped frequency distribution.**

**ans:**

**10.) Explain the following terms with suitable example.**

- Cumulative frequency distribution
- Bivariate frequency distribution
- Inclusive and exclusive method of classification
- Open end classes
- Relative frequency distribution

**ans:** The following terms are explained below with suitable example:

**Cumulative frequency distribution**:

Cumulative frequency (CF) distribution is a way of summarizing and presenting frequency data, where each entry in the table represents the cumulative frequency up to a certain class or interval.

**In other words**, A frequency distribution in which frequencies are successively added from top to bottom or bottom to top is called CFD.

**Bivariate frequency distribution**:

The frequency distributions showing the analysis of the relationship between two variables simultaneously is called Bivariate frequency distribution.

**11.) Distinguish between diagrams and graphs. What are the advantages of diagrammatic and graphical presentation of statistical data?**

**ans:** Below is a table distinguishing between diagrams and graphs:

**Advantages of Diagrammatic and Graphical Presentation of Statistical Data are:**

- Diagrams and graphs provide a clear visual representation of complex data, making it easier to understand and interpret.
- They facilitate comparison between different data sets, categories, or variables, enabling insights into patterns and trends.
- They support evidence-based decision-making by providing visual evidence.

**12.) What are the general rules for constructing diagrams?**

**ans:** The general rules for constructing diagrams include:

- Selection of scale
- Choice of a diagram
- Proportion between width and height
- Title
- Neatness and cleanliness
- Footnote
- Index
- Simplicity

**13.) What are different types of bar diagrams? Discuss their importance.**

**ans:** The different types of bar diagrams are:

**Simple bar diagrams**

**Importance**:- They are straightforward and easy to understand, making them useful for presenting basic comparisons between different categories or groups. They provide a clear visual representation of data and allow for quick comparisons of magnitudes or frequencies.

**Multiple bar diagrams**

**Importance**:- They allow for the comparison of multiple datasets or subgroups within each category or group. They provide insights into variations and patterns across different subgroups, enabling more comprehensive analysis and decision-making.

**Sub-divided or component bar diagrams**

**Importance**:- They break down each bar into segments or components, representing different parts or categories within the total value. They provide a detailed view of the composition or distribution of data, highlighting the relative contributions of each component.

**Percentage bar diagrams**

**Importance**:- They represent each bar as a percentage of the total, providing insights into the relative proportions or distributions of data. They facilitate comparisons of proportions and help identify trends or changes over time.

**14.) Write short notes on:**

- Bar diagrams
- Pie-diagrams
- Histogram
- Frequency polygon
- Frequency curve
- Ogives

**ans:** Short notes on above topics are given below:

â€£ **Bar diagrams**:

Bar diagrams, also known as bar charts or bar graphs, are graphical representations used in business statistics to present numerical data. They consist of rectangular bars of equal width.

â€£ **Pie-diagrams:**

Pie diagrams, also known as pie charts, represent data using a circular graph divided into segments, resembling slices of a pie. Each segment represents a proportion or percentage of the whole, with the size of the segment corresponding to its relative contribution to the total.

â€£ **Histogram**:

Histogram is the graphical representation of a continuous frequency distribution. It consists of a series of rectangle with no gap between them.

â€£ **Ogives**:

An Ogive curve, also known as a cumulative frequency curve or a cumulative distribution curve, is a graphical representation of cumulative frequencies or cumulative relative frequencies of continuous variable.

**15.) What do you mean by false base line? Explain its utility in graphic representation of statistical data?**

**ans:** A false baseline refers to an incorrect or misleading reference line used in a graph or chart to distort the perception of the data being presented.

The utility of a false baseline in graphic representation of statistical data is generally negative, as it can lead to misinterpretation or misrepresentation of the data.

**16.) Write short notes on the rules of constructing:**

- Diagrams
- Graphs

**ans:** Short notes on the rules of constructing:

**Diagrams**

**17.) Mention the situation where the use of each type of diagrams and graph would be appropriate.**

**ans:**