Plus One Economics-Chapter 13: Questions and Answers in English

Chapter 13

Organisation of Data.

Multi choice questions

1. Under inclusive method….
1. Upper class limit is excluded.
2. Lower class limit is excluded.
3. Lower class limit is included.
4. None of the above.

Answer:

C. Lower class limit is included..

2. Which of the following alternatives is true?

   The class midpoint is equal to:

1. The average of the upper class limit and the lower class limit.
2. The product of upper class limit and the lower class limit.
3. The ratio of the upper class limit and the lower class limit.
4. None of the above.

Answer:

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

3. Which of the following alternatives is true?

   The frequency distribution of two variables is known as:

1. Univariate Distribution.
2. Bivariate Distribution.
3. Multivariate Distribution.
4. None of the above.

Answer:

B. Bivariate Distribution.

4. Which of the following alternatives is true?

   Statistical calculations in classified data are based on:

1. the actual values of observations.
2. the upper class limits.
3. the lower class limits.
4. the class midpoints.

Answer:

D. the class midpoints

5. Which of the following alternatives is true?

   Under Exclusive method,

1. the upper class limit of a class is excluded in the class interval.
2. the upper class limit of a class is included in the class interval.
3. the lower class limit of a class is excluded in the class interval.
4. the lower class limit of a class is included in the class interval.

Answer:

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

Answer the following questions

6. To arrange things in appropriate order and to put them into homogenous groups means……..

Answer :

Classification

7. A variable is continuous when it can be taken within the range

Answer :

Any value

8. Population refers to ………

Answer :

The aggregates from which data are to be collected

9. What is classification?

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.

10. Distinguish between raw data and classified data.

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.

11. Classes can be arranged in inclusive and exclusive manner. Point out any two features which help us to distinguish them.

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.

12. Distinguish between frequency table and frequency array.

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.

13. Distinguish between univariate frequency distribution and bivariate frequency distribution.

Answer :

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

14. 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

Answer :

Table 13.1
Variables	Frequency
0	1
1	6
2	13
3	12
4	5
5	2
6	2
7	1
Total	45

15. Classification of data is a function similar to that of sorting letters in a post office. Do you agree? Explain.

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.

16. List out examples of variables and attributes in your daily life.

Answer :

Table 13.2
Variables	Attributes
Height	Caste
Weight	Sex
Marks	Marital status
Cricket score	Educational qualification

17. ‘There are some problems in preparing frequency dis- tribution on the basis of class interval’. Do you agree? Justify.

Answer :

Yes, I agree.
The following problems arise in preparing frequency distribution on the basis of class interval.


• a) Number of class intervals to be formed
• b) Size of class intervals
• c) Class limits.
18. Can there be any advantage in classifying things?.

Answer :

The advantage of classification are the following.

• 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.
19. Name the three types of series.

Answer :

• i) Individual series
• ii) Discrete series
• iii) Continuous series
20. State the meaning and example for the following.
    • i) Chronological Classification.
    • ii) Spatial Classification.
    • iii) Qualitative Classification.
    • iv) Quantitative Classification.

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 students
21. What is variable? Distinguish between a discrete and a continuous variable.

Answer :

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:


• i) Continuous and
• ii) Discrete.
A continuous variable can take any numerical value. It may take integral values (1, 2, 3, 4, …) or fractional values(\( {{\frac{ 1}{2}} } \, ,{{\frac{ 1}{3}} } \, ,{{\frac{ 2}{3 }} }\)).
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.
22. Differentiate between exclusive method and inclusive method.

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.

23. Differentiate between quantitative classification and qualitative classification.
    

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.

24. 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

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

25. Define and illustrate the inclusive and exclusive method used in classification of data.

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

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.


Table 13.6 Exclusive method
Marks	Frequency
0 – 10	5
10 – 20	7
20 – 30	10
30 – 40	8
40 – 50	3

26. 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

Answer :

Table 13.7
Marks	Frequency
20	4
25	6
30	7
35	5
40	2

27. 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.

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

28. 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

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

29. 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.

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

30. 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

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

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, 9
    12, 8, 6, 5, 15, 8, 81, 7, 4, 17, 14, 8, 6, 12

Answer :

Table 13.13
Class	Frequency
0 – 5	9
5 – 10	12
10 – 15	5
15 – 20	2
20 and above	1
Total	29

32. 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.

Answer :

• 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
33. 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

    Represent this data in the form of a frequency array table.

Answer :

Table 13.16
Blood Group	Frequency
A	9
B	6
O	12
AB	3
B+ve	5
Total	35

34. Distinguish between a discrete and continuous variables.

Answer :

Continuous variable can take any numerical value


Table 13.17
Class	Frequency
0 – 5	9
5 – 10	12
10 – 15	5

Discrete variable can take only certain value.


Table 3.18 Exclusive method
Marks	Frequency
20	4
25	6
30	7

35. 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.

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

36. 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)

Answer :

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

• 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

Number of classes

The first problem is the decision regarding the number
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.


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 :
• a) Exclusive method
• b) Inclusive method
Exclusive method: According to this method upper class limit is excluded from a class and included in the immediate next class.
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.
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