## Chapter 13

## Organisation of Data.

##### Multi choice questions

- Under inclusive method….
- Upper class limit is excluded.
- Lower class limit is excluded.
- Lower class limit is included.
- None of the above.
- Which of the following alternatives is true?
The class midpoint is equal to:

- The average of the upper class limit and the lower class limit.
- The product of upper class limit and the lower class limit.
- The ratio of the upper class limit and the lower class limit.
- None of the above.
- Which of the following alternatives is true?
The frequency distribution of two variables is known as:

- Univariate Distribution.
- Bivariate Distribution.
- Multivariate Distribution.
- None of the above.
- Which of the following alternatives is true?
Statistical calculations in classified data are based on:

- the actual values of observations.
- the upper class limits.
- the lower class limits.
- the class midpoints.
- Which of the following alternatives is true?
Under Exclusive method,

- the upper class limit of a class is excluded in the class interval.
- the upper class limit of a class is included in the class interval.
- the lower class limit of a class is excluded in the class interval.
- the lower class limit of a class is included in the class interval.
- To arrange things in appropriate order and to put them into homogenous groups means……..
- A variable is continuous when it can be taken within the range
- Population refers to ………
- What is classification?
- Distinguish between raw data and classified data.
- Classes can be arranged in inclusive and exclusive manner. Point out any two features which help us to distinguish them.
- Distinguish between frequency table and frequency array.
- Distinguish between univariate frequency distribution and bivariate frequency distribution.
- In a city 45 families were surveyed for the number of domestic appliences they used. Prepare a frequency array based on their replies as recorded below. 1, 3, 2, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 2, 4, 2, 7, 2, 0, 3, 1, 3, 3, 2, 3, 2,2,6, 1, 6, 2, 1, 5, 1, 5, 3, 4, 2, 4, 3, 4, 3
- Classification of data is a function similar to that of sorting letters in a post office. Do you agree? Explain.
- List out examples of variables and attributes in your daily life.
- ‘There are some problems in preparing frequency dis- tribution on the basis of class interval’. Do you agree? Justify.
- a) Number of class intervals to be formed
- b) Size of class intervals
- c) Class limits.
- Can there be any advantage in classifying things?.
- i) It helps in the comparison of data.
- ii) It helps to understand relationship among variables.
- iii) It makes statistical analysis easier.
- iv) It highlights significant features of data at a glance.
- Name the three types of series.
- i) Individual series
- ii) Discrete series
- iii) Continuous series
- State the meaning and example for the following.
- i) Chronological Classification.
- ii) Spatial Classification.
- iii) Qualitative Classification.
- iv) Quantitative Classification.

- What is variable? Distinguish between a discrete and a continuous variable.
- i) Continuous and
- ii) Discrete.
- Differentiate between exclusive method and inclusive method.
- Differentiate between quantitative classification and qualitative classification.

- Prepare a frequency distribution by inclusive and exclusive method for the following data.28 27 6 16 15 2 14 5 19 25 19 20 28 32 37 13 15 11 32 4 6 9 3 36 12 8 4 1 8 3 18 12 7 17 15 22 29 21 23 9 29 4 10 5 20 20 33 27 21 27 18 31 18 9 7 1 26 24 20
- Define and illustrate the inclusive and exclusive method used in classification of data.
- Daily wages of 24 workers in a factory are given be- low. Prepare a Frequency Array. 25, 40, 25, 35, 30, 25, 25, 30, 20, 35, 35, 20, 30, 20, 35, 35, 30, 25, 30, 40, 30, 20, 25, 30
- Marks obtained by 50 students in an examination are given below. Write the frequency distribution of these marks.

8, 25, 14, 7, 33, 61, 78, 54, 81, 27, 21, 18, 67, 58, 55, 21, 90, 74, 53, 38, 42, 63, 71, 19, 20, 28, 37, 41, 85, 29, 64, 79, 88, 97, 19, 21, 41, 77, 59, 69, 52, 44, 75, 81, 27, 91, 98, 39, 86, 19. - In the frequency distribution table given below the mid-values and frequencies are given. Write the cor- responding class.
13.9 Class interval Mid-value Frequency 2.5 10 7.5 12 12.5 18 17.5 15 22.5 9 27.5 15 - Marks scored by 64 students in a test paper are given below:
9 16 22 9 22 12 39 19 14 23 6

24 16 18 7 17 20 25 28 18 10 24

20 21 10 7 18 28 24 20 14 23 25

34 22 5 33 23 26 29 13 36 11 26

11 37 30 13 8 15 22 21 32 21 31

17 16 23 12 9 15 27 17 21 Prepare a frequency distribution with inclusive classes. - Prepare a frequency distribution table from the following data taking a class interval of 4. 10 17 15 22 11 16 19 24 29 11 25 26 32 14 1 20 23 2 30 12 15 18 24 39 18 15 21 28 33 38 34 13 10 16 20 22 29 19 23 31
- Prepare a frequency distribution table by taking class interval of 5 for the following data (exclusive method). 1, 10, 3, 6, 3, 2, 2, 4, 8, 3, 12, 5, 5, 2, 912, 8, 6, 5, 15, 8, 81, 7, 4, 17, 14, 8, 6, 12
- Anagha classified the students of a school on the basis of their heights as follows.

Table 13.14 Heights (in cm) Number of students (Frequency) 110 – 120 75 120 – 130 115 130 – 140 125 140 – 150 135 150 – 160 90 160 – 170 50 - a) Name the classifaction.
- b) Tell him the other ways of classification.
- c) Find the class interval and define it.
- d) State the class marks of the first and the last class.

- a) Exclusive method
- b) Inclusive method
- c) Class interval is the size of each class into which a range of a variable is divided..
- d) 10
- The blood groups of 35 students of Class XI are re- corded as follows:
Table 13.15 A +ve B +ve B A O AB O O AB +ve A B A O O A B +ve O O B AB A B +ve B B O A B O A B O A O B O - Distinguish between a discrete and continuous variables.
- Construct a frequency distribution table from the following data taking class interval of ten.
75 83 79 66 76 58 47 57 77

65 74 63 73 68 69 52 61 54

56 78 43 88 62 49 67. - While preparing a frequency distribution from the raw data, name the questions we have to address. Briefly explain in 11⁄2 pages. (Hint: Four steps in the construction of a frequency distribution)
- i) The number of classes we should have
- ii) The size of each class
- iii) Choice of the class limit
- iv) Availability of class frequencies
- a) Exclusive method
- b) Inclusive method

Unlike a continuous variable, a discrete variable can take only certain values. Its value changes only by finite "jumps". It "jumps" from one value to another but does not take any intermediate value between them.

Exclusive Method: The classes, by this method, are formed in such a way that the upperclass limit of one class equals the lower class limit of the next class. In this way the continuity of the data is maintained. That is why this method of classification is most suitable incase of data of a continuous variable.

Under the method, the upper class limitis excluded but the lower class limit of a class is included in the interval.

An example for exclusive method of frequency distribution is given below.

Discrete variable can take only certain value.

of classes into which the raw date are to be classified. In order to avoid difficulties we have to find out their range. The range is the difference between the larget and the smallest values of the variable.

Inclusive method: It includes the upper class in that class itself. Thus both class limits are parts of the class boundaries.

Answer:

**C. Lower class limit is included..**

Answer:

**A. The average of the upper class limit and the lower class limit.**

Answer:

**B. Bivariate Distribution.**

Answer:

**D. the class midpoints**

Answer:

**A. the upper class limit of a class is excluded in the class interval.**

##### Answer the following questions

Answer :

Classification

Answer :

Any value

Answer :

The aggregates from which data are to be collected

Answer :

Classification of data is a technique with the help of which data is arranged into different groups or classes according to some common characteristics so as to facilitate the tabulation, analysis and interpretation.

Answer :

Raw data is the collected information in the form of numerical facts. It is the data collected as it is without any processing. The raw data is summurised and made comprehensible is known as classified data.

Answer :

EXclusive method: in this method the classes are found in such a way that the upper limit of one class equals the lower limit of next class. In this way, the continuity of data is maintained. This method is most suitable in case of data of a continuous variable. In this method, the upper class limit is excluded and lower and lower class limit is included in the interval.

Inclusive method : This method does not exclude the upper class limit in a class interval. Thus, both class limits are parts of the class interval.

Answer :

Frequency table is the classification of the data for a continuous variable. Frequency array is the classification of the data for a discrete variable.

Answer :

The frequency distribution of a single variable is called univariate distribution. The frequency distribution of two variables is known as bivariate frequency distribution.

Answer :

Table 13.1 | |
---|---|

Variables | Frequency |

0 | 1 |

1 | 6 |

2 | 13 |

3 | 12 |

4 | 5 |

5 | 2 |

6 | 2 |

7 | 1 |

Total | 45 |

Answer :

Yes, I do agree with the statement that the classifi- cation of data is a function similar to that of sorting letters in a post office.

The process of arranging data in groups or classes according to similarities is technically called classification. The classification is somewhat similar to that of sorting letters in a post office. Letters collected in a post office are sorted into different lots on geographical basis. They are then put in separate bags. Thus by classification we are trying to make different groups with similar characteristics. Units having a common characteristic are place in one class and the whole data are thus divided into a number of classes.

Answer :

Table 13.2 | |
---|---|

Variables | Attributes |

Height | Caste |

Weight | Sex |

Marks | Marital status |

Cricket score | Educational qualification |

Answer :

Yes, I agree.

The following problems arise in preparing frequency distribution on the basis of class interval.

Answer :

The advantage of classification are the following.

Answer :

Answer :

###### i) Chronological Classification:

In Chronological classification, data are classified either in ascend- ing or in descending order with reference to time such as years, quarters, months, weeks, etc. Example: population of India from 1951 to 2011.###### ii) Spatial Classification:

In Spatial Classification the data are classified with reference to geographical locations such as countries, states, cities, districts, etc. Example: yield of wheat in different state of India.###### iii) Qualitative Classification:

Attributes can be classified on the basis of either the presence or the absence of a qualitative characteristic. Such a classification of data on attributes is called a Qualitative Classification. Example: grouping of people on the basis of gender.###### iv) Quantitative Classification:

When the collected data of such characteristics are grouped into classes, the classification is a Quantitative Classification.Example: marks obtained by studentsAnswer :

A simple definition of variable does not tell you how it varies. Different variables vary differently and depend- ing on the way they vary, they are broadly classified into two types:

Unlike a continuous variable, a discrete variable can take only certain values. Its value changes only by finite "jumps". It "jumps" from one value to another but does not take any intermediate value between them.

Answer :

Under the exclusive method, the upper class limit is excluded but the lower class limit of a class is in- cluded in the interval.

On the otherhand, under the inclusive method, the upper class limit is included in the class interval.

Answer :

Classification done according to quantitative variet- ies like marks and wages etc. is termed as quantita- tive classification. On the otherhand, classification according to attributes like honesty and beauty is known as qualitative classification.

Answer :

Table 13.3 Frequency distribution by inclusive method | |
---|---|

Class interval | Frequency |

1 – 7 | 15 |

8 – 14 | 12 |

15 – 21 | 15 |

22 – 28 | 9 |

29 – 35 | 7 |

36 – 42 | 2 |

Table 13.4 Frequency distribution by exclusive method | |
---|---|

Class interval | Frequency |

1 – 8 | 15 |

8 – 15 | 12 |

15 – 22 | 15 |

22 – 29 | 9 |

29 – 36 | 7 |

36 – 42 | 2 |

Answer :

Inclusive Method: In comparison to the exclusive method, the Inclusive Method does not exclude the upper class limit in a class interval. It includes the upper class in a class. Thus both class limits are parts of the class interval.

An example for inclusive method of frequency distribution is given below.Table 13.5 Inclusive method | |
---|---|

Marks | Frequency |

0 – 9 | 5 |

10 – 19 | 7 |

20 – 29 | 10 |

30 – 39 | 8 |

40 – 49 | 3 |

Under the method, the upper class limitis excluded but the lower class limit of a class is included in the interval.

An example for exclusive method of frequency distribution is given below.

Table 13.6 Exclusive method | |
---|---|

Marks | Frequency |

0 – 10 | 5 |

10 – 20 | 7 |

20 – 30 | 10 |

30 – 40 | 8 |

40 – 50 | 3 |

Answer :

Table 13.7 | |
---|---|

Marks | Frequency |

20 | 4 |

25 | 6 |

30 | 7 |

35 | 5 |

40 | 2 |

Answer :

13.8 Frequency Distribution with Tally Mark | ||
---|---|---|

Class | Tally Marks | Marks |

0 – 20 | //// /// | 8 |

20 – 40 | //// //// // | 12 |

40 – 60 | //// //// | 10 |

60 – 80 | //// //// / | 11 |

80 – 100 | //// //// | 9 |

Answer :

13.10 | ||
---|---|---|

Class interval | Mid-value | Frequency |

0 – 5 | 2.5 | 10 |

5 – 10 | 7.5 | 12 |

10 – 15 | 12.5 | 18 |

15 – 20 | 17.5 | 15 |

20 – 25 | 22.5 | 9 |

25 – 30 | 27.5 | 15 |

Answer :

Table 13.11 Inclusive method | |
---|---|

Marks | Frequency |

1 – 8 | 5 |

9 – 16 | 17 |

17 – 24 | 26 |

25 – 32 | 11 |

33 – 40 | 5 |

Total | 64 |

Answer :

13.12 Frequency Distribution with Tally Mark | ||
---|---|---|

Class | Tally Marks | Marks |

10 – 14 | //// / | 6 |

14 – 18 | //// /// | 8 |

18 – 22 | //// // | 7 |

22 – 26 | //// // | 7 |

26 – 30 | //// | 5 |

30 – 34 | //// | 4 |

34 – 38 | / | 1 |

38 – 42 | // | 2 |

N = 40 |

Answer :

Table 13.13 | |
---|---|

Class | Frequency |

0 – 5 | 9 |

5 – 10 | 12 |

10 – 15 | 5 |

15 – 20 | 2 |

20 and above | 1 |

Total | 29 |

Answer :

Answer :

Table 13.16 | |
---|---|

Blood Group | Frequency |

A | 9 |

B | 6 |

O | 12 |

AB | 3 |

B+ve | 5 |

Total | 35 |

Answer :

Continuous variable can take any numerical value

Table 13.17 | |
---|---|

Class | Frequency |

0 – 5 | 9 |

5 – 10 | 12 |

10 – 15 | 5 |

Table 3.18 Exclusive method | |
---|---|

Marks | Frequency |

20 | 4 |

25 | 6 |

30 | 7 |

Answer :

13.19 Frequency Distribution with Tally Mark | ||
---|---|---|

Class | Tally Marks | Marks |

40 – 50 | /// | 3 |

50 – 60 | //// | 5 |

60 – 70 | //// /// | 8 |

70 – 80 | //// // | 7 |

80 – 90 | // | 2 |

N = 25 |

Answer :

While preparing a frequency distribution the follow- ing four points need to be taken into account:

###### Number of classes

The first problem is the decision regarding the numberof classes into which the raw date are to be classified. In order to avoid difficulties we have to find out their range. The range is the difference between the larget and the smallest values of the variable.

###### The size of each class

We can determine the class intervel once we decide about the number of classes. Thus these two deci- sions are interlinked with one another.###### The choice of class limits

The choice of class limits is important in forming frequency distribution. There are two methods for construction of a frequency distribution. They are :Inclusive method: It includes the upper class in that class itself. Thus both class limits are parts of the class boundaries.

###### Adjustment in class interval

In order to ensure the continuity of variable, we can change the inclusive calsses into exclusive classes. For this, find the difference between the lower limit of the second class and the upper limit of the first class. Divide the difference obtained by two.