BACHELOR'S DEGREE PROGRAMME
TermEnd Examination, June, 2012
ELECTIVE COURSE: COMMERCE
ECO7: ELEMENTS OF STATISTICS
Time: 2 hours Maximum Marks: 50
Note: Attempt any four questions. All questions carry equal marks.
1. (a) Fill in the blanks with the appropriate word chosen from those given in the brackets. 5
(i) Ogive helps in locating the value of Median. (median/ mode)
(ii) The units of each class should normally be Homogeneous. (heterogeneous/homogeneous)
(iii) A time series is an arrangement of statistical data in chronological order. (chronological/Random)
(iv) Harmonic mean is the reciprocal of the mean of reciprocals. (mean/median)
(v) Range is easy to compute and short in nature. (short/comprehensive)
(b) State whether the statements given below are True or False. 5
(i) Statistics is the science of estimates and probabilities. True
(ii) Hybrid ratios are usually stated in percentage form. False
(iii) Secondary data should never be accepted without careful enquiry. True
(iv) "Random sampling" is a synonym of a representative sample. False
(v) In any sample survey, there are less chances of errors. False
(c) Distinguish between biased and unbiased error. 2½
2. (a) What is sampling? What are the essentials of a good sample? 6½
Ans: Meaning of Sampling: Sampling refers to the statistical process of selecting and studying the characteristics of a relatively small number of items from a relatively large population of such items,, to draw statistically valid inferences about the characteristics about the entire population.
Characteristics of the sampling technique (Essentials of a Good sampling)
In order to reach at right conclusions, a sample must possess the following essential characteristics.
1. Representative: The sample should truly represent the characteristics of the verse. For this investigator should be free from bias and the method of collection should be appropriate.
2. Adequacy: The size of the sample should be adequate i.e., neither too large nor small but commensurate with the size of the population.
3. Homogeneity: There should be homogeneity in the nature of all the units selected for the sample. If the units of the sample are of heterogeneous character it will impossible to make a comparative study with them.
4. Independent ability: The method of selection of the sample should be such that the items of the sample are selected in an independent manner. This means that lection of one item should not influence the selection of another item in any manner d that each item should be selected on the basis of its own merit.
(b) Eleven students of a class obtained the following marks in Accountancy. Calculate the Quartile deviation and its coefficient. 6
5, 8, 10, 15, 22, 25, 26, 29, 30, 31 and 35.
Solution:
X
 
5
8
10
15
22
25
26
29
30
31
35

3. (a) A car owner purchases petrol for his car at Rs. 2.40, Rs. 2.80 and Rs. 3.00 per litre respectively for three months. If his expenditure for three months is Rs. 480, Rs. 518 and Rs. 540 respectively, find the average price of petrol purchased during three months. 6
Solution:
Price

Average Expenditure

Qnty.
 
2.40
2.80
3.00

480
518
540

(b) Find the coefficient of skewness if difference of two Quartiles is 8, sum of two quartiles is 22 and median is 10.5. 6½
4. The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking, it was found that one item with a value of 8 was incorrect. Calculate the correct mean and standard deviation if
(a) the wrong item is omitted, and 6.5
(b) it is replaced by 12. 6
Solution: Given,
If wrong items is omitted
Correct
Now, Correct
Again, Correct
(b) if wrong item 8 is replaced by 12
5. (a) What is meant by dispersion? What are the methods of computing measures of dispersion? Illustrate the practical utility of these methods. 7
(b) Below are given the net profits (in thousand rupees) of a business for 5 years. 5½
Year

2006

2007

2008

2009

2010

Net profit

10

15

17

20

28

Draw a Lorenz Curve
6. (a) Calculate median and mode of the following series. 5+5
No. of days Absent below

5

10

15

20

25

30

35

40

45

No. of students

29

224

465

582

634

644

650

653

655

Solution:
6. (a)
No. of days
(less than)

No. of
Students

Class Interval

Frequency
 
5
10
15
20
25
30
35
40
45

29
224
465
582
634
644
650
653
655

0 – 5
5 – 10
10 – 15
15 – 20
20 – 25
25 – 30
30 – 35
35 – 40
40 – 45

29
195 f0
14 f1
117 f2
52
10
6
3
2

Mode class = ( 10 – 15 )
Now,

N = 655

(b) Discuss the general rules for tabulation 2½
Ans: Principles of Tabulation (General Rules of tabulation)
There are no hard and fast rules for preparing a statistical table. Prof. Bowley has rightly pointed out “In collection and tabulation, common sense is the chief requisite and experience is the chief teacher.” However, the following points should be borne in mind while preparing a table.
(i) A good table must contain all the essential parts, such as, Table number, Title, Head note, Caption, Stub, Body, Foot note and source note.
(ii) A good table should be simple to understand. It should also be compact, complete and selfexplanatory.
(iii) A good table should be of proper size. There should be proper space for rows and columns. One table should not be overloaded with details. Sometimes it is difficult to present entire data in a single table. In that case, data are to be divided into more number of tables.
(iv) A good table must have an attractive get up. It should be prepared in such a manner that a scholar can understand the problem without any strain.
(v) Rows and columns of a table must be numbered.
(vi) In all tables the captions and stubs should be arranged in some systematic manner. The manner of presentation may be alphabetically, or chronologically depending upon the requirement.
7. Distinguish between the following:
(a) Simple Table and Complex table. 4
(b) Discrete series and continuous series. 4½
Ans: Quantitative variables can be further classified as discrete or continuous. If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable. Some examples will clarify the difference between discrete and continuous variables.
Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.
Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We could not, for example, get 2.3 heads. Therefore, the number of heads must be a discrete variable.
(c) Simple Arithmetic Mean and Weighted Arithmetic Mean. 4
Ans: Mean: It is a concept that is required to know the overall performance or phenomenon. If there are 10 boys in a class having different weights, we calculate their mean weight by adding up their individual weights and then divide the total by 10 to arrive at the average weight of the class. Thus average is the sum of all individual observations divided by the number of observations.
Weighted Mean: Basically, weighted mean is also an average with a slight difference that not all observations carry equal weights. If different observations carry different importance, or weights in this case, each observation is multiplied by its weight and then added up. This is done to take into account importance of different observations as they carry significance more than others. Unlike simple average, where all the observations carry same value, in weighted average, every observation is assigned a different Weightage and thus the average is calculated keeping in mind the importance of each observation. The concept will be come clear from the following example.