REG NO:

ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – MARCH/APRIL 2016

B.COM (T.T.)– II SEMESTER

C2 15 AR 203 :BUSINESS STATISTICS

Duration: 3 Hours Max. Marks: 100

SECTION – A

Answer ALL the questions. Each carries 2 marks. (10×2=20)

Give the meaning of Statistics.

Three students in a group of 9 failed in the examination. Six students who passed got the marks as 55, 40, 82, 61, 80, and 53. Find the Median.

Define Index Number.

Mention the four components of Times Series.

The average rainfall for a week excluding Sunday was 0.5”. Due to heavy rain on Sunday, the average rain for the week was 1.5. How much rainfall was there on Sunday?

State any two differences between Correlation and Regression Analysis.

What are the different methods of constructing Price Index Numbers?

Explain with a help of scatter diagram perfect negative and positive correlation.

Find the range and coefficient of range from the following:

10.

Mention any two basic functions of MS-Excel.

SECTION – B

II)

Answer any FOUR questions. Each carries 5 marks. (4×5=20)

11.

Prepare a frequency distribution of the marks obtained by 50 students in an examination with width of each class interval as 10. Use exclusive method of classification:

57	44	80	75	00	18	45	14	04	64
72	51	69	34	22	83	70	20	57	28
96	56	50	47	10	34	61	66	80	46
22	10	84	50	47	73	42	33	48	65
10	34	66	53	75	90	58	46	39	69

12.

Define Statistics and explain its characteristics in detail.

13.

Calculate the trend values by the method of 4-yearly moving averages:

Year

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

Sales

(Rs)

464

515

518

467

502

540

557

571

586

612

Sales are given in Lakhs of rupees.

14.

Compute the cost of living index number using both the Aggregate Expenditure Method and Family Budget Method from the following information:

Commodity	Unit Consumption in Base Year	Price in Base Year	Price in Current Year
Wheat	200	20	24
Rice	50	30	35
Pulses	50	40	45
Ghee	20	200	300
Sugar	40	25	30
Oil	50	100	120
Fuel	60	50	62.5
Clothing	40	500	600

15.

Compute Spearman’s rank correlation for the following observation:

Candidate	1	2	3	4	5	6	7	8
Judge X	20	22	28	23	30	31	21	24
Judge Y	28	24	22	25	26	27	32	30

Marks are awarded out of 35.

16.

The Shareholders Research Centre of India has conducted recently a research-study on price behavior of three leading industrial shares A, B and C for the period 2011 to 2016. The results are published in the Quarterly Journal:

Share	Average Price	Standard Deviation	Current Selling Price
A	18.2	5.4	36.00
B	22.5	4.5	34.75
C	24.0	6.0	39.00

The above figures are given in Rs.

(a) Find Coefficient of Variation & state which share appears to be more stable in value?

(b) If you are the holder of all the three shares, which one would you like to dispose of at present, and why?

SECTION – C

III)

Answer any THREE questions. Each carries 15 marks. (3×15=45)

17.

Find the standard deviation and coefficient of variation from the following data: (use step deviation method)

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of Students	12	18	35	42	50	45	20	8

18.

(a)The following table gives the distribution of items of production and also the relatively defective items among them, according to size groups. Find the correlation coefficient between size and percentage of defective items and its probable error. (Use Karl Pearson’s Assumed Mean Method)

Size-group	15-16	16-17	17-18	18-19	19-20	20-21
No. of Items	200	270	340	360	400	300
No. of Defective Items	150	162	170	180	180	114

(b)Using the following data construct Fisher’s Ideal Index and show that it satisfies Factor Reversal test and Time Reversal test:

Commodity	Price (in Rs.) per unit		Number of units
Commodity	Base Year	Current Year	Base Year	Current Year
A	6	8	10	12
B	10	10	5	8
C	5	7	8	10
D	15	20	12	15
E	20	25	15	10

(8+7)

19.

(a)Draw a histogram using graph for the following distribution and find the modal wage. Also check the value by direct calculation.

Daily wages (in Rs.)	200-220	220-240	240-260	260 -280	280-300	300-320	320-340
No. of workers	60	140	110	150	120	100	90

(b)“Statistical tools are very helpful in numerous troubles of various fields such as agricultural production, population, industrial growth, sociology, psychology, administration, natural science, etc. Universal application of statistics does not mean that it is free from limitations”. – In the light of this statement briefly discuss the limitations of Statistics.

(10 +5)

20.

(a) Calculate the value of Mode for the following data (use Grouping Method):

Marks	10	15	20	25	30	35	40
Frequency	8	12	36	35	28	18	9

(b) A computer while calculating the correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results:

n = 25; ∑X = 125; ∑X² = 650; ∑Y = 100; ∑Y²= 460; ∑XY = 508

It was however, discovered at the time of checking that he had copied down two pairs as:

X	Y
6	14
8	6

While the correct values were:

X	Y
8	12
6	8

Obtain the correct value of coefficient of correlation using assumed mean method. (8+7)

21.

Below are given the annual production (in thousand tonnes) of a fertilizer factory:

Year	2010	2011	2012	2013	2014	2015	2016
Production	70	75	90	91	95	98	100

(a) Fit a straight line trend by the method of least squares and depict the trend line on the graph.

(b) Estimate the trend value of production for the year 2017.

SECTION – D

Case Study – Compulsory question. (1×15=15)

22.

From the data given below find:

(a) The two regression equations.

(b) The coefficient of correlation between marks in Economics and Statistics.

Marks in Economics	25	28	35	32	31	36	29	38	34	32
Marks in Statistics	43	46	49	41	36	32	31	30	33	39

&&&&&&&&&&&&&&&&&&&&&&&&&&

Latest Govt Job & Exam Updates:

St. Joseph’s College of Commerce II Sem Business Statistics Question Paper PDF Download

View Full List ...