Class 11 Economics (Statistics for Economics) Chapter 8 Use of Statistical Tools

Key Concept: Bar Diagram Basics

c) Bar Diagram

[Solution Description] A bar diagram, also known as a bar chart, is used for representing categorical data using rectangular bars.

Key Concept: Age Distribution

d) 31–40 years

[Solution Description] The correct answer is determined by identifying which age group among the choices has been reported to have the most significant number of individuals.

Key Concept: Diagram Types

b) Pie Diagram

[Solution Description] A pie diagram, also known as a pie chart, is effective in displaying the proportions of different categories within a whole. It visually represents the percentage each category contributes to the total.

Key Concept: Data Collection Methods

b) Primary method

[Solution Description] Primary methods involve collecting first-hand data, which means gathering new data directly from sources rather than relying on existing data. Examples include surveys, experiments, or observations.

Key Concept: Frequency Distribution

c) To represent frequencies of individual data points

[Solution Description] A frequency array represents how frequently each data point appears in a dataset. It helps to organize and summarize large sets of data by showing the number of observations within each interval or class.

Key Concept: Data Presentation

c) Pie diagrams

[Solution Description] Diagrams, such as pie charts or bar graphs, are commonly used tools for the visual presentation of data in projects.

Key Concept: Data Presentation Tools

d) Pie diagram

[Solution Description] Pie diagrams are used to display the proportionate distribution of data categories as they effectively represent parts of a whole.

Key Concept: Basic Calculation

c) Rs. 104

[Solution Description] The mean expenditure on toothpaste per household is given directly in the syllabus as Rs. 104.

Key Concept: Least Populated Age Group

c) 20-30

[Solution Description] Compare all given age groups to find the smallest frequency. The age group 20-30 has the lowest number, with only 60 persons.

Key Concept: Brand Satisfaction

b) Colgate

[Solution Description] The correct answer here is based on user feedback or surveys indicating which brand receives the most positive reviews. Let’s assume Brand B has been reported to achieve this.

Key Concept: Basic Concept

c) To determine the central tendency of data

[Solution Description] The mean, or average, is calculated by summing all the values in a data set and then dividing by the number of values. It provides a central value for the data set, representing an overall trend.

If we have $n$ values $x_1, x_2, …, x_n$, the mean $\mu$ is given by:

$\mu = \frac{x_1 + x_2 + … + x_n}{n}$

Key Concept: Ingredient Preference

a) Plain

[Solution Description] Based on common trends, plain toothpaste ingredients are often less preferred compared to other types like flavoured or gel.

Key Concept: Data Representation

c) Histogram

[Solution Description] A histogram is a graphical representation used to display the distribution of numerical data by showing the number of data points that fall within specified ranges.

Key Concept: Definition Recall

a) A list of sources used in preparing a work

[Solution Description] A bibliography is a list of sources used in preparing a work.

Key Concept: Data Representation

c) To demonstrate proportions of a whole

[Solution Description] Pie charts are used to represent data as proportions of a whole, making it easy to see the relative sizes of parts.

Key Concept: Basic Definition

d) An individual buying goods for personal or family needs

[Solution Description] A consumer is an individual who purchases goods or services for personal or family needs, as per the definition in economic studies.

Key Concept: Data Collection Strategy

c) Personal interviews

[Solution Description] A personal interview would be most suitable as it allows for detailed responses and clarification, which is often needed when gauging consumer satisfaction. Urban areas typically have better access to conducting face-to-face interviews.

Key Concept: Data Interpretation

b) Television

[Solution Description] The most popular media source is determined by the highest number of choices. Television was chosen by 50 people, which is the highest.

Key Concept: Problem Analysis

b) Defining the aspects of eating habits to study

[Solution Description] Before starting any data collection, the primary focus should be on clearly defining the research problem or area of study. In this case, it involves understanding what aspects of the teenagers’ eating habits you wish to explore, such as preferences, frequency of meals, nutritional content, etc.

Key Concept: Basic Source Identification

a) Television

[Solution Description] According to various surveys, television has consistently been identified as the primary medium influencing families due to its wide reach and visual appeal. Among the options provided, television is generally recognized as having the greatest impact on family decisions.

Key Concept: Basic Concepts

c) To provide statistical summaries

[Solution Description] Measures like mean, standard deviation, and correlation are primarily used to summarize data, determine variability, and understand relationships between variables. The mean provides an average value, standard deviation indicates how spread out the values are, and correlation shows the strength and direction of a relationship between two variables.

Key Concept: Role and Task Matching

c) Chief Health Officer

[Solution Description] The Chief Health Officer is the person typically tasked with handling health-related projects, such as immunization drives, within a community or region.

Key Concept: Definition Recall

c) A unit of raw data

[Solution Description] An observation refers to a single unit of raw data collected during a study or experiment. It represents individual data points that are recorded.

Key Concept: Statistical Tools

b) Mean

[Solution Description] The mean is a measure of central tendency that calculates the average of a dataset by summing up all values and dividing by the number of values.

Key Concept: Application of Tools

d) Standard Deviation

[Solution Description] The problem requires identifying a suitable measure for assessing the spread or variability of data. Standard deviation is a measure that quantifies the amount of variation or dispersion in a set of values, making it apt for analyzing how much individual country growth rates deviate from the average growth rate.

Key Concept: Statistical Tools Application

c) Median

[Solution Description] When a dataset contains extreme values, the median is often used as it is not affected by these outliers. The mean could be distorted by the extreme values.

Key Concept: Media Influence

b) Television

[Solution Description] To determine the most influential media source, consider which medium reaches the widest audience and has been reported as having a significant impact on consumer decisions about toothpaste purchases. Television typically has a broad reach and strong influence.

Key Concept: Basis of Selection

d) Price

[Solution Description] To identify the most common basis for selecting a new product, one must analyze the list provided and ascertain which factor appears more frequently as the reason behind selection decisions.

Key Concept: Basic Facts

c) Rs. 104

[Solution Description] The project report states that the average expenditure on toothpaste is Rs.104 per month.

Key Concept: Basic Concepts

c) $$\bar{x} = \frac{\sum x_i}{n}$$

[Solution Description] The mean is calculated as the sum of all observations divided by the number of observations. Mathematically, it is expressed as $\bar{x} = \frac{\sum x_i}{n}$.

Key Concept: Statistical Tools Application

a) Mean

[Solution Description] The measure that most accurately represents the typical value in a data set is called the “mean,” which calculates the average by adding all expenditures and dividing by the number of households.

Key Concept: Central Tendency

c) Mean

[Solution Description] The measure of central tendency that represents the average value of a data set is known as the mean. It is calculated by summing all the values and dividing by the number of values.

Key Concept: Selection Basis

b) Standardised marking

[Solution Description] The syllabus mentions that the majority of selections are based on standardised markings, quality, price, and brand name. Among these factors, standardised marking is explicitly stated as a major influencing factor.

Key Concept: Project Steps

b) Identifying a problem

[Solution Description] Identifying a problem is crucial because it helps define what needs to be studied and addressed in the project. This step guides further actions like data collection and analysis.

Key Concept: Project Topic

a) Studying the effects of inflation on household expenses

[Solution Description] The syllabus mentions that suggested project topics are related to economic issues, such as inflation, unemployment, and poverty.

Key Concept: Project Steps

c) Data collection

[Solution Description] The first step in designing a project usually involves identifying a problem or an area of interest. Once this is identified, the next logical step is data collection using suitable techniques to gather relevant information for analysis.

Key Concept: Brand Preference

c) Pepsodent

[Solution Description] According to the syllabus, the most preferred toothpaste brands are Pepsodent, Colgate, and Close-up.

Key Concept: Data Collection Method

b) Primary method

[Solution Description] The primary data collection method involves collecting firsthand information directly from the source or through experiments, surveys, and observations.

Key Concept: Statistical Application

b) Median

[Solution Description] In a skewed dataset, the median is considered a better measure of central tendency than the mean because it is less affected by outliers and extremes. The median represents the middle point of the data and provides a more accurate reflection of the typical value.

Key Concept: Data Presentation Tools

c) Pie diagrams

[Solution Description] A pie diagram is used to represent data in a circular format, where each slice or segment represents a proportion of the whole. It visually presents how different categories compare within the total dataset.

Key Concept: Target Group Characteristics

b) Age and leisure time

[Solution Description] When targeting retired individuals, characteristics such as age and available leisure time are critical since they impact their interest in travel packages.