Maths And Stats

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(As this blog site does not support the formatting, there could be errors in the post.
This series is compiled from various resources on net. I have made changes wherever necessary to make it simple to understand. )
Table: Frequency distribution of heights of 50 students

Height Frequency (Number of students)
144.5-146.5 2
146.5-148.5 5
148.5-150.5 8
150.5-152.5 15
152.5-154.5 9
154.5-156.5 6
156.5-158.5 4
158.5-160.5 1
Total 50

Class, class limits, class boundaries

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(As this blog site does not support the formatting, there could be errors in the post.
This series is compiled from various resources on net. I have made changes wherever necessary to make it simple to understand. )
Table: Frequency distribution of heights of 50 students

Height Frequency (Number of students)
144.5-146.5 2
146.5-148.5 5
148.5-150.5 8
150.5-152.5 15
152.5-154.5 9
154.5-156.5 6
156.5-158.5 4
158.5-160.5 1
Total 50

Class, class limits, class boundaries

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(As this blog site does not support the formatting, there could be errors in the post.
This series is compiled from various resources on net. I have made changes wherever necessary to make it simple to understand. )

Ex 1
The marks secured by 60 students of a class are given below

46, 57, 23,5,12 53, 38,58,26,43
36, 63,26,48,76 45, 66,74,16,86
56, 31,58,90,32 43, 36,66,46,58
36, 59,54,48,21 36, 64,58,45,76
58, 84,68,65,59 74, 48,64,58,50
46, 53,64,57,65 58, 95,56,66,44

Construct a frequency distribution table.

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(As this blog site does not support the formatting, there could be errors in the post.
This series is compiled from various resources on net . I have made changes wherever necessary to make it simple to understand. )

CHAPTER 2
Measures of Central Tendency And Dispersion

2.1 Introduction

In this chapter we will study various types of data, methods of data collection , data representation and measures of central tendency.

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In censuses and large scale surveys, enumerators (persons who collect data are called as enumerators) are engaged to collect information from the persons concerned. They gather information in schedules or questionnaire specially prepared for the purpose in the form of answers given by the respondents to specific questions.

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It should be noted that the information collected through questions should be such that it is usable.

Advantages:

• It can be administered to large groups of individuals.
• It is much less time consuming and is economical.
• A much larger coverage can be made as people in distant places can be reached without much difficulty.
• It is advantageous in a situation where the persons concerned move to far away places. For example, in an enquiry relating to old students of a collage, such a method may be useful as students move out and away after leaving the institution.

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Questionnaires are usually administered on paper, in a structured or semi-structured format. Respondents often choose from among a set of forced-choice, or provided, responses. These can include yes/no or scaled responses. Questionnaires can be administered in person, by mail, over the phone, or via email/Internet.

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The indirect personal investigation is through some agencies that have intimate knowledge of the phenomenon under enquiry. For example, an investigator may collect information about cost of cultivation indirectly from village head instead of collecting the information from farmers.

Advantages:

• It is less time consuming and expensive.
• As information can be collected from more knowledgeable persons, these are expected to be more useful and reliable.
• As fewer persons need be contacted, the enquiry could be more extensive than in case of direct personal enquiry.

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Dispersion on the other hand is about, as in above case, whether majority of students have scored marks near the average or far away from the average. For example average of 1 and -1 is 0. Similarly average of 100 and -100 is also 0. In the first case data values are near the average i.e dispersion is less while in the second case data values are more scattered or spread or away from the average i.e dispersion is more. The most common measure of dispersion is the standard deviation

2.2 Methods of collection of primary data*