TermEnd Examination: June, 2014
ECO7: ELEMENTS OF STATISTICS
Note: Attempt any four questions. All questions carry equal marks.
1. (a) Fill in the blanks with a suitable word as given in the brackets: 8
(i) The sum of the deviations of the individual item from X is always Zero. (one/zero)
(ii) Random sampling method provides equal chance to every item of the population for being included in the sample. (Random/NonRandom)
(iii) Inaccuracy due to arithmetical miscalculation is termed as an error. (an error/ a mistake)
(iv) The decimal part in the value of common logarithm is called Mantissa. (characteristic/ Mantissa)
(v) Schedule Method of data collections is suitable, where informants are illiterates. (Schedule/Questionnaire)
(vi) Attribute refers to Qualitative aspect of data. (quantitative/qualitative)
(vii) A histogram helps in determining the value of Median. (median/mode)
(viii) Harmonic Mean is the reciprocal of the mean of reciprocals. (Mean/Harmonic Mean)
(b) Distinguish between classification and tabulation. 4½
Ans: The process of arranging the data in groups or classes according to their common characteristics is technically known as classification. Classification is the grouping of related facts into classes. It is the first step in tabulation. Tabulation refers to the systematic arrangement of the information in rows and columns. Rows are the horizontal arrangement. In classification, data are separated and grouped based on a property of the data common to all values. In tabulation, data is arranged into columns and rows based on characteristics/properties, or indicators. Tabulation often emphasize on the presentation aspects of the data, while classification is used as a means of sorting of data for further analysis.
2. What is a statistical survey? Describe the steps to be involved in organising a statistical survey. 12½
Ans: Meaning of Statistical Survey: A Statistical Survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect information about units in a population and it involves asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors.
Stages of Statistical Survey
Statistical surveys involve two stages namely: Planning and Execution. Figure shows the two broad stages of Statistical Survey.
1. Planning a Statistical Survey: The relevance and accuracy of data obtained in a survey depends upon the care taken in planning. A properly planned investigation can lead to the best results with least cost and time. Figure gives the explanation of steps involved in the planning stage.
2. Execution of statistical survey: Controlled methods should be adopted at every stage of carrying out the investigation to check the accuracy, coverage, methods of measurements, analysis and interpretation. The collected data should be edited, classified, tabulated and presented in the form of diagrams and graphs. The data should be carefully and systematically analysed and interpreted.
Methods for collecting data : Collection of data is done by a suitable method as per the following:
1. Direct personal observation
2. Indirect oral interview
3. Information through agencies
4. Information through mailed questionnaires
5. Information through a schedule filled by investigators
3. (a) Draw percentage subdivided bar diagram for the following data: 8
Results of B.com

No. of students
 
2007 – 08

2008 – 09
 
First Division
Second Division
Third Division
Unsuccessful

50
200
300
150

90
300
400
200

Total

700

990

(b) State the disadvantage of secondary data. 4½
Ans: Secondary Data: Data which are collected by someone else, used in investigation are knows as Secondary data. Data are primary to the collector, but secondary to the user. For example: Statistical abstract of the Indian Union, Monthly abstract of statistics, Monthly statistical digest, International Labour Bulletin (Monthly).
Demerits of Secondary Data:
(a) Degree of accuracy may not be acceptable.
(b) Secondary Data may or may not fit the need of the project.
(c) Data may be influenced by personal bias of investigator.
4. Compute mode from the following data: 12½
Daily wages (Rs.) :

1520

2025

2530

3035

3540

4045

4550

No. of workers :

12

23

19

14

5

4

3

Solution:
Class Interval

Frequency
 
15 – 20
20 – 25
25 – 30
30 – 35
35 – 40
40 – 45
45 – 50

12 = f0
23 = f1
19 = f2
14
5
4
3

Modal class = ( 20 – 25 )
Now, modal

5. (a) Calculate combined standard deviation from the following data: 8
Particulars

Firm A’

Firm B’

No. of workers
Mean Wages (Rs.)
Standard Deviation (Rs.)

600
48
9.49

700
42
10.95

Solution:
Combined mean
Page – 2
Again,
(b) Explain the law of Inertia of large numbers. 4½
Ans: Law of Inertia of large numbers, in statistics, the theorem that, as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean. The law of large numbers was first proved by the Swiss mathematician Jakob Bernoulli in 1713. He and his contemporaries were developing a formal probability theory with a view toward analyzing games of chance. Bernoulli envisaged an endless sequence of repetitions of a game of pure chance with only two outcomes, a win or a loss. Labeling the probability of a win p, Bernoulli considered the fraction of times that such a game would be won in a large number of repetitions. It was commonly believed that this fraction should eventually be close to p. This is what Bernoulli proved in a precise manner by showing that, as the number of repetitions increases indefinitely, the probability of this fraction being within any prespecified distance from p approaches 1.
6. (a) What do you mean by observation method of data collection? State its two merits and two limitations. 6½
Ans: Observation Method: It is watching other persons’ behaviour as it actually happens without controlling it. It enables understanding significant events affecting social relations of the participants. It determines reality from the viewpoint of the observed person/Researcher.
Advantages of Observation method:
1. It is less complicated and less timeconsuming.
2. It offers data when respondents are unable or unwilling to cooperate for giving information.
3. It allows collection of wide range of information.
Disadvantages of Observation method
1. In natural setting, control over variables is not possible that affect the data.
2. The data collected through observation cannot be quantified. It is difficult to categorise indepth emotional and humanistic data.
3. Observational studies use a smaller sample than survey studies.
(b) Compute harmonic mean from the data given below: 6
Commodity

Price in Kg. per Rs.

Quantity bought (kgs.)

A
B
C

2
5
10

10
20
30

Solution:
H.M
7. (a) The mean and standard deviation of a set of 100 observations were 40 and 5 respectively. But, by mistake, the value of one of the observations was taken as 50 instead of 40. Find the correct mean and variance. 8
Solution: Given wrong
Now, Wrong
Correct
Therefore Correct Mean
Again, Wrong
Correct
Therefore, Correct
(b) What do you mean by Primary data? Give an example of primary data. 4½
Ans: Primary Data: Data which are collected for the first time for a specific purpose are known as Primary data. Primary data are collected directly from the people related to enquiry. These data are more reliable and accurate.
For example: Population census, National income collected by government, Textile Bulletin (Monthly), Reserve bank of India Bulletin (Monthly) etc.