Class 11 Economics (Statistics for Economics) Chapter 3 Organisation Of Data

Key Concept: Basic Formula

b) 45

[Solution Description] To find the class midpoint, we use the formula $\text{Class Midpoint} = \frac{\text{Upper Class Limit} + \text{Lower Class Limit}}{2}$. Here, the upper class limit is 50 and the lower class limit is 40.

So,

$\text{Class Midpoint} = \frac{50 + 40}{2} = \frac{90}{2} = 45$.

Key Concept: Class Interval Calculation

c) 10

[Solution Description]

Class width or class interval is calculated as the difference between the upper and lower class limits. Here, it’s $20 – 10 = 10$.

Key Concept: Differentiation

b) Bivariate considers two variables, while univariate involves only one variable

[Solution Description] Univariate frequency distributions involve only one variable, whereas bivariate frequency distributions consider two variables simultaneously to explore relationships between them.

Key Concept: Tally Basics

c) Groups of 5

[Solution Description] In tally marking, tallies are grouped in sets of 5 to make it easier to count them quickly.

Key Concept: Basic Definition

c) To summarize bivariate data

[Solution Description] A bivariate frequency distribution aims to summarize and analyze data that involves two variables, allowing us to understand the relationship between them.

Key Concept: Class Interval Recognition

a) Equal

[Solution Description] To determine if the intervals are equal, we compare their sizes.

For 25-35: Size = $35 – 25 = 10$

For 10-20: Size = $20 – 10 = 10$

Both intervals have the same size, so they are equal.

Key Concept: Definition Recall

c) Classification based on geographical locations

[Solution Description] Spatial Classification refers to organizing and categorizing data based on geographical locations or spatial attributes.

Key Concept: Real-world Application

b) Quantitative Classification

[Solution Description] The classification based on age groups is an example of quantitative classification because the data is divided into numerical intervals.

Key Concept: Purpose of Classification

c) To organize data for better comprehension

[Solution Description] Classifying raw data helps in organizing large sets of data into manageable sections, making it easier to comprehend and analyze.

Key Concept: Example Identification

b) Height of a student

[Solution Description] Continuous variables are those which can assume all possible values within a range. Height is a typical example since it can be measured accurately up to several decimal points.

Key Concept: Qualitative vs Quantitative

b) Religion

[Solution Description] A qualitative characteristic refers to non-numeric attributes like religion, color, or nationality.

Key Concept: Adjustment Calculation

b) 1

[Solution Description] To find the adjustment value, divide the gap between the classes by 2. Here, the adjustment is $\frac{2}{2} = 1$.

Key Concept: Unequal Class Interval Analysis

b) To better represent data concentration

[Solution Description] Unequal class intervals are often employed when there is a significant variation in data concentration. This method helps better represent the data by amplifying areas where data points are densely packed and using wider intervals where data points are sparse.

Key Concept: Class Mark Understanding

b) 15

[Solution Description] The class mark is calculated as the average of the lower and upper boundaries of the class interval. For the interval 10-20, this is: $\frac{10 + 20}{2} = 15$.

Key Concept: Simple Comparison

b) It is easier to analyze

[Solution Description] Classified data is organized into categories, making it easier to analyze and draw insights compared to raw data, which is often unorganized and large.

Key Concept: Simple Application

b) Discrete variable

[Solution Description] The number of cars is counted in whole numbers without fractional parts, indicating it is a discrete variable. Discrete variables only take certain individual values.

Key Concept: Basic Classification

b) It summarizes data into classes with frequencies

[Solution Description] A frequency distribution table organizes data into classes and shows the number of occurrences in each class. It helps in understanding how frequently different values occur within a dataset.

Key Concept: Frequency Definition

c) 5

[Solution Description]

The frequency of a data point in a dataset refers to how many times that particular number appears. Here, the number 15 appears 5 times, so the frequency of the number 15 is 5.

Key Concept: Classification Purpose

b) To organize raw data for ease of analysis

[Solution Description] Classifying data simplifies complex datasets, making trends and patterns easier to identify, and facilitates efficient data handling.

Key Concept: Relative Frequency

b) 0.25

[Solution Description] Relative frequency is calculated as the frequency of the class divided by the total frequency. Thus, $\text{Relative Frequency} = \frac{15}{60} = 0.25.$

Key Concept: Frequency Count

c) 20

[Solution Description] Frequency refers to the total count represented by tally marks. If there are 20 tally marks, the frequency is the same as the number of tally marks, which is 20.

Key Concept: Class Interval Identification

b) 10-20

[Solution Description] An exclusive class interval does not include the upper limit in the interval. For example, if we take the interval 10-20 as exclusive, it includes numbers from 10 up to but not including 20.

Key Concept: Basic Definition

c) To enhance clarity and ease analysis

[Solution Description] The primary purpose of classifying data is to organize it in a manner that allows for easier analysis and interpretation, facilitating statistical computations and decision-making.

Key Concept: Class Mark Calculation

b) 60

[Solution Description]

To find the class mark of a class interval, we calculate the average of the upper and lower boundaries of the interval. For the interval 50-70:

$\text{Class Mark} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} = \frac{50 + 70}{2} = \frac{120}{2} = 60$

Therefore, the class mark is $60$.

Key Concept: Time Order

c) 2001

[Solution Description] This question requires identifying the specific year when the population reached 84 crores. You would need to refer to the data where such information is documented in chronological order.

Key Concept: Frequency Distribution Understanding

b) Exactly 15 data points lie between 20 and 30.

[Solution Description] The frequency distribution table shows how many observations fall within each class interval. Here, having 15 observations in the class interval 20-30 implies that 15 data points lie between and include 20 up to but not including 30.

Key Concept: Class Limits

c) Lower limit 30, Upper limit 40

[Solution Description]

In a class interval, the lower class limit is the smallest value that can belong to the class, and the upper class limit is the largest value. For the given class interval 30–40, the lower class limit is 30 and the upper class limit is 40.

Key Concept: Class Interval Width

b) 10

[Solution Description]

To find the width of a class interval, subtract the lower limit from the upper limit. For the interval 25–35:

$\text{Width} = 35 – 25 = 10$

Thus, the width of the class interval is 10.

Key Concept: Classification Purpose

b) It facilitates easier analysis and interpretation.

[Solution Description] Classification allows data to be organized systematically, making it easier to draw conclusions and perform analysis. By grouping similar items together, it enhances clarity and reduces complexity.

Key Concept: Definition Recall

b) Frequency distribution of two variables

[Solution Description] A bivariate frequency distribution is a type of statistical analysis that shows the frequency or number of occurrences of two different variables simultaneously in a table format.

Key Concept: Frequency Count

b) 10

[Solution Description] The frequency of the class interval 50-60, as given in the problem, is 10.

Key Concept: Frequency Distribution

c) Tally marking

[Solution Description] Tally marking is a simple and effective method used to count frequencies when constructing frequency distribution tables. It consists of making marks that are easily counted after all data entries have been recorded.

Key Concept: Class Limits

d) 45 and 55

[Solution Description]

The class limits define the range of values in a class interval. In this case, the lower class limit is 45 and the upper class limit is 55.

Key Concept: Class Mark Calculation

b) 65

[Solution Description] The class mark of an interval is calculated as the average of the lower and upper limits of the interval. For the interval 60-70, the class mark is calculated as follows:

$\text{Class Mark} = \frac{60 + 70}{2} = 65$

Hence, the class mark for the interval 60-70 is 65.

Key Concept: Classification Methods

b) Inclusive Method

[Solution Description] The inclusive method considers both the upper and lower class limits when forming classes in a frequency distribution.

Key Concept: Basic Definition

c) To record frequency of occurrences

[Solution Description] Tally marking is used to keep track of frequency counts when organizing raw data into categories or classes. It helps in easily counting and categorizing the data for further analysis.

Key Concept: Class Limits

b) Exclusive

[Solution Description]

To determine if the method is exclusive, verify if either the upper or lower limit is excluded. In the interval 20-30, the value 30 is excluded and goes into the next interval.

Key Concept: Definition Recall

b) Frequency distribution of two variables

[Solution Description] A Bivariate Frequency Distribution is defined as the frequency distribution involving two variables, allowing us to understand the relationship between these variables.

Key Concept: Basic Concept

b) The difference between the upper class limit and the lower class limit

[Solution Description] The class interval in a frequency distribution is calculated as the difference between the upper class limit and the lower class limit.

Key Concept: Definition Recall

b) To bring order and facilitate analysis

[Solution Description] Classifying raw data helps to organize it, making it easier to analyze and interpret in statistical terms.

Key Concept: Class Midpoint

a) The average of the upper class limit and the lower class limit

[Solution Description]

The class midpoint is calculated as the average of the upper and lower class limits. It is given by the formula:

$\text{Class Midpoint} = \frac{\text{Upper Class Limit} + \text{Lower Class Limit}}{2}$

For example, if the lower class limit is 10 and the upper class limit is 20, the class midpoint would be:

$\text{Class Midpoint} = \frac{20 + 10}{2} = 15$

Therefore, the correct answer is option a.

Key Concept: Unequal Class Intervals

b) To better represent data concentration

[Solution Description] Unequal class intervals are often used when data points are concentrated in particular ranges, allowing for better representation of data concentration. This helps in highlighting areas where data is dense and avoids overrepresentation or underrepresentation of certain segments.

Key Concept: Definition Recall

c) It makes raw data manageable and easier to analyze

[Solution Description] Classification brings order to raw data, making it easier to handle and analyze.

Key Concept: Simple Classification

a) Continuous, Discrete, Continuous

[Solution Description]

– Distance traveled: Continuous (because it can be measured precisely, including fractions).

– Number of apples: Discrete (as it involves counting whole apples).

– Temperature: Continuous (since it can take any value within a range).

Based on these classifications:

– Continuous variables are those like distance traveled and temperature.

– Discrete variables are those like the number of apples.

Key Concept: Basic Concept Identification

c) Chronological Classification

[Solution Description] Chronological classification is a method where data is arranged or categorized according to different periods or times.

Key Concept: Unequal Class Interval Application

b) When data is concentrated in certain ranges

[Solution Description] Unequal class intervals are often used when data is concentrated in certain ranges. This allows for a clearer representation of the distribution where some areas have more data concentration compared to others.

Key Concept: Exclusive Method

a) Upper class limit

[Solution Description]

In the exclusive method of class intervals, the upper class limit is usually not included in the interval, meaning observations equal to the upper class limit are counted in the next higher class.

Key Concept: Class Mark Calculation

c) 15

[Solution Description] The class mark is calculated by taking the average of the upper and lower class limits. For the class interval 10-20:

$\text{Class Mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2} = \frac{10 + 20}{2} = 15$

Key Concept: Class Limit Identification

b) 25

[Solution Description] The lower class limit is the smallest value that can belong to the class interval. For the class interval 25-35, the lower class limit is 25.

Key Concept: Frequency Definition

b) To classify and analyze discrete variables

[Solution Description] A frequency array is primarily used to classify and represent data related to discrete variables for better analysis.