BACHELOR'S DEGREE PROGRAMME
TermEnd Examination December, 2011
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)Dispersion is based upon the Second averages of the order. [third/second]
(ii)Geometric mean gives Precise result as it is rigidly defined. [Indefinite/ precise]
(iii)Classification is a process of statistical analysis while tabulation is a way of presenting Data. [Data/ Derivatives]
(iv)Median is that value of the variable which divides the group into Two equal parts. [Four/Two]
(v) For obtaining the value of quartile deviation, we divide the difference between first and third quartiles by two. [Balance/Difference]
(b) State whether the statements given below are True or False. 5
(i)Every average has its own peculiar characteristics. It is difficult to say as to which average is the best. True
(ii)Graphs are generally a pictorial representation of facts through lines or curves. False
(iii)If the series is plotted on a graph paper and a bell shaped curve emerges, the skewness shall be present. False
(iv) Range increases or decreases with the value of sample. True
(v)Dispersion shows the scatteredness of items in a series while skewness relates to the properties of its shape. True
(c) Explain the relationship between median and mode. 2½
2. (a) Karl Pearson's coefficient of skewness for a distribution is — 0.7 and the values of median and standard deviation are 12.8 and 6 respectively. Determine the value of mean. 5
Ans: Given coefficient of Skewness =  0.7
Median = 12.80
S.D. = 6
Now, Coefficient of Skewness
(b)What are the criteria of a satisfactory measure of central tendency? Discuss the standard measures and state as to which of these is a satisfactory criteria. 5
Ans: The following are the important properties which a good average should satisfy
 It should be easy to understand.
 It should be simple to compute.
 It should be based on all the items.
 It should not be affected by extreme values.
 It should be rigidly defined.
 It should be capable of further algebraic treatment.
Different standard for measuring
There are three measures of central tendency and each one plays a different role in determining where the center of the distribution or the average score lies.
a) Mean: First, the mean is often referred to as the statistical average. To determine the mean of a distribution, all of the scores are added together and the sum is then divided by the number of scores.
b) Median: The median is another method for determining central tendency and is the preferred method for highly skewed distributions. The media is simply the middle most occurring score.
c) Mode: Finally, the mode is the least used measure of central tendency. The mode is simply the most frequently occurring score.
The mean is the preferred measure of central tendency because it is used more frequently in advanced statistical procedures; however, it is also the most susceptible to extreme scores. It consists of almost all the essentials of a good measure of central tendency.
(c)Explain the utility of statistics in business. 2½
Ans: The utility of statistics in business:
(i) It presents fact in a definite form. Numerical expressions of data are convincing.
(ii) It simplifies mass of figures. The data presented in the form of table, graph or diagram, average or coefficients are simple to understand.
(iii) It facilitates comparison. Once the data are simplified they can be compared with other similar data.
(iv) It helps in prediction. Plans and policies of organisations are invariably formulated in advance at the time of their implementation.
(v) It helps in the formulation of suitable policies. Statistics provide the basic material for framing suitable policies.
3. (a) How are the mean and median affected when it is known that for a group of ten students scoring an average of 60 marks and the best paper was wrongly marked 80 instead of 75 ? 4
Ans: Given, Wrong Mean = 60, N = 10
Now,
Correct ∑x
Again, Median is an Average of Position and it is not affected if last value is wrong.
(b)If arithmetic mean and geometric mean of two values are 10 and 8 respectively find the values. 4
Ans: Given, AM= 10, GM = 8
Let the two numbers be x and y.
Now, AM of two given Numbers
Again, GM of the two given numbers
(c)What is Lorenz Curve? Describe as to how a Lorenz curve is constructed, and discuss its uses. 4½
Ans: Lorenz curve is the form of a curve which is derived from the cumulative percentage of the given variables. This curve was given by Dr. Max O. Lorenz a popular Economic Statistician. He studied distribution of Wealth and Income with its help. It is graphic method to study dispersion. It helps in studying the variability in different components of distribution especially economic. The base of Lorenz Curve is that we take cumulative percentages along X and Y axis. Joining these points we get the Lorenz Curve. Lorenz Curve is of much importance in the comparison of two series graphically. It gives us a clear cut visual view of the series to be compared.
Describe steps to plot 'Lorenz Curve'
 Cumulate both values and their corresponding frequencies.
 Find the percentage of each of the cumulated figures taking the grand total of each corresponding column as 100.
 Represent the percentage of the cumulated frequencies on X axis and those of the values on the Y axis.
 Draw a diagonal line designated as the line of equal distribution.
 Plot the percentages of cumulated values against the percentages of the cumulated frequencies of a given distribution and join the points so plotted through a free hand curve.
Purpose of Lorenz curve: It is a cumulative distribution function especially referring to the income distribution of a population. A often used coefficient of income inequality is the gini coefficient which is a measure to the deviation of the actual cumulative income distribution from what would be obtained if everyone had the same income.
4. (a) Explain any three important methods used for diagrammatic representation of data. 4½
Ans: Most common graphs in statistics are listed below:
 Pareto Diagram or Bar Graph  A bar graph contains a bar for each category of a set of qualitative data. The bars are arranged in order of frequency, so that more important categories are emphasized.
 Pie Chart or Circle Graph  A pie chart displays qualitative data in the form of a pie. Each slice of pie represents a different category.
 Histogram  A histogram in another kind of graph that uses bars in its display. This type of graph is used with quantitative data. Ranges of values, called classes, are listed at the bottom, and the classes with greater frequencies have taller bars.
(b) Make a frequency table having grades of wages with classintervals of two rupees each from the following data of daily wages received by 30 labourers in a certain factory, and then compute the average daily wages paid to labourers. Daily wage in Rs. 8
14, 16, 16, 14, 22, 13, 15, 24, 12, 23, 14, 20, 17, 21, 18, 18, 19, 20, 17, 16, 15, 11, 12, 21, 20, 17, 18, 19 22 23

5. (a) A particular model of a radio set carries the following pricetags: 5
Rs. 210, 220, 225, 225, 225, 235, 240, 250, 270, 280 .Calculate mean deviation of prices.
Ans: Calculation of Mean deviation
X
 
210
220
225
225
225
235
240
250
270
280

28
18
13
13
13
3
2
12
32
42

Mean
Now, M.D.
(b) Coefficient of variation of two series are 58 and 69. Their standard deviations are 21.2 and 15.6 respectively. What are their arithmetic means? 7½
Ans: Given,
Set 1 Set 2
Coefficient of variation = 58 69
Standard Deviation = 21.2 15.6
Mean = ? ?
6. (a) Write a short note on the editing of data. 4
(b)What is statistical error? How does it differ from mistake? 4
(c)Write a short note on Degree of Accuracy. 4½
7. Calculate the mean and standard deviation from the following distribution of weekly wages of 5,000 employees of a factory. 12½
Wages (Rs.)

5055

4550

4045

3540

3035

2530

2025

No. of workers

250

300

400

450

800

1100

1700

Ans: Calculation of Mean and SD
Wages

f

X (midvalue)

d

d’

d’2

fd’2

fd’

20 – 25
25 – 30
30 – 35
35 – 40
40 – 45
45 – 50
50 – 55

1,700
1,100
800
450
400
300
250

22.50
27.50
32.50
37.50
42.50
47.50
52.50

15
10
5
0
+5
+10
+15

3
2
1
0
+1
+2
+3

9
4
1
0
1
4
9

15,300
4,400
8,00
0
400
1,200
2,250

5,100
2,200
800
0
400
600
750

N = 5,000

25

24,350

6,350

Assumed Mean = 37.50 (A)
Now, Mean
Again,