LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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FIRST SEMESTER – November 2008
ST 1500 – STATISTICAL METHODS
Date : 10-11-08 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A (10×2=20)
Answer ALL the questions
- What is a census survey?
- Identify the scale used for each of the following variables
- Calories consumed during the day.
- Marital status.
- Perceived health status reported as poor, fair, good or excellent.
- Blood type
- Mention any four measures of dispersion.
- Give a measure of kurtosis.
- State the principle of least squares.
- What is the standard form of growth curves?
- When will the regression lines be perpendicular to each other?
- If the regression coefficients are bXY = – 0.4 and bYX = – 0.9 find the
correlation coefficient between X and Y.
- What is a dichotomous classification?
- State the relation between Yule’s coefficient of association and
coefficient of colligation.
PART – B (5×8=40)
Answer any FIVE questions
- Describe any two methods of collecting primary data along with their
merits and demerits.
- Explain the importance of diagrammatic representation of data.
- Compute mean and median for the following frequency distribution
Sales target : 10-20 20-30 30-40 40-50 50-60
(Rs.lakhs)
No. of times
achieved : 6 8 12 9 5
- The sum and sum of squares corresponding to length X (in cm) and weight Y (in gms) of 50 tapioca tubers are given below:
∑X = 212, ∑X2 = 902.8, ∑Y = 261, ∑Y2 = 1457.6
Which is more varying, the length or weight?
- Measurements of serum cholesterol (mg/100ml) and arterial calcium deposition (mg/100g dry weight of tissue) were made on 12 animals. The data are as follows:
Calcium
(X) : 59 52 42 59 24 24 40 32 63 57 36 24
Cholesterol
(Y) : 298 303 233 287 236 245 265 233 286 290 264 234
Calculate the correlation coefficient.
- The equations of the two regression lines obtained in a correlation
analysis are as follows:
3X+12Y = 19, 3Y+9X = 46
Obtain i) the value of correlation coefficient.
- ii) Mean values of X and Y.
iii) Ratio of the coefficient of variability of X to that of Y.
- What do you understand by consistency of given data? Examine the
consistency of the following data:
N = 1000, (A) = 600, (B) = 500, (AB) = 50, the symbols having their
usual meanings.
- In a certain investigation carried on with regard to 500 graduates and 1500 non-graduates, it was found that the number of employed graduates was 450 while the number of unemployed non-graduates was 300.
In the second investigation 5000 cases were examined. The number of
non-graduates was 3000 and the number of employed non-graduates was
- The number of graduates who were found to be employed was
- Calculate the coefficient of association between graduates and
employment in both the investigations. Can any definite conclusion be
drawn from the coefficients?
PART – C (2×20=40)
Answer any TWO questions
- Draw a Histogram for the following frequency distribution of output produced by 190 workers in a firm and use it to find an approximate value of the mode. Also verify it using the formula.
Output in units : 300-310 310-320 320-330 330-340 340-350
No. of workers : 9 20 24 38 48
Output in units : 350-360 360-370 370-380
No. of workers : 27 17 7
- Calculate a measure of dispersion and a measure of skewness based on quartiles from the following distribution:
Wages (Rs.): below 35 35-37 38-40 41-43 over 43
No.of wage
earners : 14 60 95 24 7
- Consider the following data where x is temperature (in oc) and Y is the number of eggs per cm2 .
X : 3 5 8 14 21 25 28
Y : 2.8 4.9 6.7 7.6 7.2 6.1 4.7
Fit a quadratic equation to these data.
- Various dose of a poisonous substance were given to groups of 25 mice and the following results were observed:
Dose(mg): 4 6 8 10 12 14 16
Number
of deaths: 1 3 6 8 14 16 20
Find the equation of the regression lines. Estimate the number of deaths
in a group of 25 mice who receive a 7-milligram dose of this poison.
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