LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – NOVEMBER 2010
ST 1502/ST 1500 – STATISTICAL METHODS
Date : 10-11-10 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL the questions [10×2=20]
- State any two limitations of statistics.
- Write down the types of Scaling with examples.
- Define measures of central tendency.
- What do you mean by skewness?
- Write down the normal equations for the exponential curve.
- What is curve fitting?
- State the assumptions underlying in Karlpearson’s correlation co-efficient.
- Define probable error.
- Examine the consistency of the following data:
N= 1000; (A)= 600; (B)= 500; (AB)= 50.
- Write the Yule’s Coefficient of association between the attributes.
PART – B
Answer any FIVE questions [5×8=40]
- Describe the various types of diagrammatic representation of data.
- Draw the cumulative frequency curve. find the quartiles for the following data:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| No of Students | 4 | 8 | 11 | 15 | 12 | 6 | 3 |
- Find the missing frequencies using the median value 46 for the following data:
| Variable | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | Total |
| Frequency | 12 | 30 | ? | 65 | ? | 25 | 18 | 219 |
- The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation √13.44. Find the standard deviation of the second group.
- Show that the correlation coefficient cannot exceed unity.
- Obtain a straight line trend equation by the method of least squares. Find the value for the
missing year 1961.
| Year | 1960 | 1962 | 1963 | 1964 | 1965 | 1966 | 1969 |
| Value | 140 | 144 | 160 | 152 | 168 | 176 | 180 |
- Find the association of A and B in the following cases:
- N = 1000; (A)= 470; ( B)= 620 and (AB)= 320
- (A)= 490; (AB)= 294; (α)= 570 and (αβ)= 380
- (AB)= 256; (αB)= 768; ( Aβ)= 48 and ( αβ)= 144.
- Find the angle between the two regression lines.
PART – C
Answer any TWO questions [2×20=40]
- a) Describe the various types of classification and tabulation of data in detail. (12)
- b) A cyclist pedals from his house to his college at a speed of 10Kmph and back from
the college to his house at 5Kmph. Find the average speed. (8)
- a) For a distribution, the mean is 10, variance is 16, γ1 is +1 and β2 is 4. Obtain
the first four moments about the origin. Make a comment on distribution.
- b) Calculate i) Quartile Deviation and ii) Mean Deviation from mean for the
following data:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| No of Students | 6 | 5 | 8 | 15 | 7 | 6 | 3 |
- a) The following table gives, according to age, the frequency of marks obtained by 100 students
in an intelligence test: Calculate the Correlation Coefficient.
| Age | 18 | 19 | 20 | 21 | Total |
| Marks | |||||
| 10-20 | 4 | 2 | 2 | 0 | 8 |
| 20-30 | 5 | 4 | 6 | 4 | 19 |
| 30-40 | 6 | 8 | 10 | 11 | 35 |
| 40-50 | 4 | 4 | 6 | 8 | 22 |
| 50-60 | 0 | 2 | 4 | 4 | 10 |
| 60-70 | 0 | 2 | 3 | 1 | 6 |
| Total | 19 | 22 | 31 | 28 | 100 |
- b) Predict the value of Y when X=6 for the following data:
Σx=55; Σxy=350; Σy=55; Σx2=385 and n=10.
- a) Fit an exponential curve of the form Y=abx to the following data:
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Y | 1.0 | 1.2 | 1.8 | 2.5 | 3.6 | 4.7 | 6.6 | 9.1 |
- b) 800 candidates of both sex appeared at an examination. The boys outnumbered the
girls by 15% of the total. The number of candidates who passed exceed the number
failed by 480. Equal number of boys and girls failed in the examination.
Prepare a 2×2 table and find the coefficient of association. Comment on the result.
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