Gujarat Board Statistics Class 11 GSEB Solutions Chapter 2 Presentation of Data Ex 2 Textbook Exercise Questions and Answers.

## GSEB Textbook Solutions Class 11 Statistics Chapter 2 Presentation of Data Ex 2

**Section – A**

MCQ Questions

MCQ Questions

Choose the correct option from those given below each question:

### Question 1.

Which of the following variables is discrete?

(a) Height of a person

(b) Weight of a commodity

(c) Area of a ground

(d) Number of children per family

**Answer:**(d) Number of children per family

### Question 2.

Which of the following variables is continuous?

(a) Number of errors per page of a book

(b) Number of cars produced

(c) Number of accidents on road

(d) Monthly income of a person

**Answer:**(d) Monthly income of a person

### Question 3.

Name the method of classification of raw data related to daily demand of a product.

(a) Classification of attribute data

(b) Classification of numeric data

(c) Raw distribution

(d) Manifold classification

**Answer:**(b) Classification of numeric data

### Question 4.

Name the type of classification of the data related to the occupation and education of a person living in a certain region.

(a) Tabulation

(b) Classification of numeric data

(c) Raw distribution

(d) Discrete frequency distribution

**Answer:**(a) Tabulation

### Question 5.

In continuous frequency distribution, what is the class length of a class?

(a) Average of two successive lower boundary points.

(b) Average of class limits.

(c) Difference between upper boundary point and lower boundary point of that class.

(d) Average of upper boundary point and lower boundary point of the class.

Answer:

(c) Difference between upper boundary point and lower boundary point of that class.

### Question 6.

Range of an ungrouped data is 55 and it is divided into 6 classes. Then, what is the class length?

(a) 10

(b) 9

(c) 9.17

(d) 10.17

Answer:

(a) 10

### Question 7.

Inclusive classes for a distribution are 10- 19.5, 20-29.5, 30-39.5. What are the exclusive class limits for the second class?

(a) 19.5 – 29.5

(b) 19.75 – 29.75

(c) 20 – 30

(d) 19-29

Answer:

(b) 19.75 – 29.75

### Question 8.

A discrete variable has values 0, 1, 2, 3, 4 with the respective frequency 2, 4, 6, 8, 14. What is the value of ‘more than’ type cumulative frequency when the value of variable is 2?

(a) 28

(b) 12

(c) 34

(d) 6

Answer:

(a) 28

### Question 9.

A continuous distribution has classes 0-9, 10- 19, 20-29, 30-39 with the respective frequencies 10, 20, 40, 10. What is the less than type cumulative frequency for the boundary point 29.5?

(a) 30

(b) 50

(c) 70

(d) 80

Answer:

(d) 80

### Question 10.

For a continuous variable, classes are 1 – 1.95; 2-2.95; 3-3.95; 4-4.95; 5-5.95, then what is the lower boundary point of the second class?

(a) 1.995

(b) 2

(c) 2.975

(d) 1.975

Answer:

(d) 1.975

### Question 11.

Which of the following statements is /are true?

Statement 1: A method of representing the

large and complex data in simple and attractive manner is called diagram.

Statement 2: Self-explanatory representation of main characteristics of the data is called diagram.

Statement 3: Representation of comparative study of data is called diagram,

(a) Only statement 1 is true.

(b) Only statements 1 and 2 are true.

(c) Statements 1, 2 and 3 are true.

(d) All three statements are false.

**Answer:**(c) Statements 1, 2 and 3 are true.

### Question 12.

The class intervals for a continuous variable are 0-99, 100-199, 200-299, 300-399, 400-499. What is the mid-value of the second s class?

(a) 149.5

(b) 150

(c) 199.5

(d) 99.5

**Answer:**(a) 149.5

### Question 13.

What do we call a table that shows designation, gender and marital status of employees of a company?

(a) Simple classification

(b) Classification of numeric data

(c) Manifold classification

(d) Simple table

**Answer:**(c) Manifold classification

### Question 14.

Which of the following diagrams is used to represent sub-data of classified information?

(a) Bar diagram

(b) Divided bar diagram

(c) Multiple bar diagram

(d) Pictogram

**Answer:**(b) Divided bar diagram

### Question 15.

Which of the following diagrams is used for comparing the sub-data of the classified data?

(a) Pictogram

(b) Pie chart

(c) Bar diagram

(d) Divided bar diagram

**Answer:**(b) Pie chart

## Section – B

Very Short Answer

Answer the following question in one sentence :

### Q1. Define discrete variable.

A discrete variable is one that can take on specific, countable values within a defined range.

### Q2. Define continuous variable.

A continuous variable is a variable that can take on any value within a specified range.

### Q3. What is classification?

Classification is the process of organizing ungrouped or raw data in a systematic and concise manner.

### Q 4. State the types of classification.

Classification is divided into two types: quantitative classification and qualitative classification.

### Q 5. Define the frequency of observation.

The frequency of observation is a numeric value representing the repetition of a particular observation. It is denoted by the symbol.

### Q 6. State the method to determine the number of classes on the basis of the range of data and class length.

Number of classes = $\frac{\text { range }}{\text { class length }}$

### Q 7. When should one form a frequency distribution with unequal class lengths?

One should form a frequency distribution with unequal class lengths when the range of raw or ungrouped data is very large.

**Q 8: Define cumulative frequency.**

Cumulative frequency is the sum of frequencies up to the value of an observation or a class in a frequency distribution. It is denoted by symbol ‘*cf*.’

### Q 9. Define ‘less than’ type cumulative frequency distribution for discrete data.

A table showing ‘less than’ cumulative frequency corresponding to the various values of discrete data is called ‘less than’ type cumulative frequency distribution.

### Q 10: Define ‘more than’ type cumulative frequency distribution for continuous data.

A table showing ‘more than’ cumulative frequency corresponding to the lower boundary point of various classes is called ‘more than’ type cumulative frequency distribution for continuous data.

### Q 11: Write a formula for finding the mid-value of a class.

Mid Value of a class =$\frac{\text { upper limit of class + lower limit of class }}{2}$

### Q 12. Define tabulation.

Tabulation is the process of arranging qualitative data in a systematic manner into rows and columns.

### Q13. Define manifold classification.

Manifold classification is the classification of raw data based on more than one attribute.

### Q 14. What is the characteristic of the best table to represent qualitative data?

The characteristic of the best table to represent qualitative data is that the table satisfies the objective of classification.

### Q 15. What is the main disadvantage of the classification of data?

The main disadvantage of the classification of data is that it changes the basic form of the individual unit of the data.

### Q 16. In statistical study, what is the main objective of a diagram?

In statistical study, the main objective of a diagram is to represent the huge and complex data into a simple, attractive, and concise form.

## Section – C

Descriptive Answers

Answer the following questions as required:

### Q1. Define quantitative and qualitative data.

Quantitative data:

- Quantitative data consists of numerical information, representing measurable quantities associated with a variable—either discrete or continuous.
- This type of data deals with objective, quantifiable information that can be expressed in terms of numbers.
- Examples include height, weight, income, and temperature.

**Qualitative data**:

- Qualitative data involves non-numerical qualities or characteristics and is collected based on qualitative variables or attributes.
- These variables cannot be precisely measured with numbers.
- Examples include colors, opinions, and types of fruits.

### Q 2. Define discrete frequency distribution with illustration.

A discrete frequency distribution is a summary of the occurrences of distinct values in a dataset, where each value is paired with its frequency.

**OR.**

A table showing the frequency corresponding to various values of discrete variable is called discrete frequency distribution.

For example, consider a class with students and the number of pets they own:

Number of Pets x | 0 | 1 | 2 | 3 | 4 |

Number of students f | 5 | 8 | 10 | 4 | 3 |

In this representation, the table shows how many students have 0, 1, 2, 3, or 4 pets.

Another example, Discrete frequency distribution showing the number of children in 100 families

Number of Children x | 0 | 1 | 2 | 3 | Total |

Number of Families f | 5 | 30 | 45 | 20 | 100 |

### Q 3. Define continuous frequency distribution with illustration.

A table showing the frequency corresponding to various classes of continuous variable is called continuous frequency distribution. It is prepared, when the range of data is very large.

**OR**

A continuous frequency distribution summarizes data within intervals or ranges. For example, consider a dataset of individual heights:

Height (in inches) | Frequency |
---|---|

60-65 | 7 |

65-70 | 12 |

70-75 | 20 |

75-80 | 15 |

80-85 | 10 |

This table shows the frequency of individuals within specified height intervals, offering a concise overview of the height distribution in the population.

Another example: Continuous frequency distribution showing the height of 50 students of Std. XI

Height (in cm) | 90-100 | 100-110 | 110-120 | 120-130 | 130-140 | Total |

Number of Students f | 3 | 8 | 12 | 17 | 1o | 50 |

### Q 4. Explain the definition of inclusive continuous frequency distribution.

An inclusive continuous frequency distribution is when the classes in a frequency distribution have unequal upper and lower limits, and the upper limit of one class is included in that class.

For example, if you have classes like 10-19, 20-29, 30-39, where the upper limit of one class (e.g., 29) is included in that class and the lower limit of the next class (e.g., 30) is not equal to the upper limit of the previous class, then it’s called an inclusive continuous frequency distribution.

Class Interval | Frequency |
---|---|

10-19 | 20 |

20-29 | 30 |

30-39 | 40 |

40-49 | 25 |

50-59 | 15 |

**Key points to remember:**

**Unequal upper and lower limits:**The class intervals have different lower and upper limits, creating distinct ranges for each class.**Upper limit inclusion:**The upper limit of each class is considered part of that class. For example, the value 29 belongs to the class 20-29.**No overlapping classes:**The lower limit of each class is always one more than the upper limit of the previous class. This prevents any values from falling into multiple classes.

### Q 5. Write formulae for obtaining class boundary points from inclusive class limits.

**Lower Boundary Point (LBP)**

$\text{LBP}i$ = $\frac{\text{Lower Limit}_i + \text{Upper Limit}{i-1}}{2}$

**Upper Boundary Point (UBP) **

$\text{UBP}i$ = $\frac{\text{Lower Limit}{i+1} + \text{Upper Limit}_i}{2}$

These formulas provide a simple way to calculate the average values that define the boundaries of a class interval.

The lower boundary point $\text{LBP}i$ of the $i^{th}$ class is the average of the lower limit of the current class $\text{Lower Limit}_i$ and the upper limit of the class preceding it $\text{Upper Limit}{i-1}$.

The upper boundary point $\text{UBP}i$ of the $i^{th}$ class is the average of the lower limit of the following class $\text{Lower Limit}{i+1}$ and the upper limit of the current class $\text{Upper Limit}_i$.