# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

# B.Sc. DEGREE EXAMINATION – STATISTICS

First SEMESTER – NOVEMBER 2003

** ****ST 1500/ STA 500 STATISTICAL METHODS**

07.11.2003 Max: 100 Marks

9.00 – 12.00

**section ****–**** A**** **

*Answer ALL questions* (10 ´ 2 = 20 Marks)

- Give the definition of statistics according to Croxton and Cowden.
- Comment on the following: “ Sample surreys are more advantageous than census”.
- Give an example for

(i) Quantitative continuous data (ii) Discrete time series data

- Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
- Mention any two limitations of geometric mean.
- From the following results obtained from a group of observations, find the standard deviation. S(X-5) = 8 ; S(X-5)
^{2 }= 40; N = 20.

- For a moderately skewed unimodal distribution, the A.M. is 200, the C.V.

is 8 and the Karl Pearson’s coefficient of skewness is 0.3. Find the mode

of the distribution.

- Given below are the lines of regression of two series X an Y.

5X-6Y + 90 = 0

#### 15X -8Y-130 = 0

Find the values of .

- Write the normal equations for fitting a second degree parabola.
- Find the remaining class frequencies, given (AB) = 400;

(A) = 800; N=2500; (B) = 1600.

### SECTION – B

*Answer any FIVE questions*. (5 ´8 = 40 Marks)

- Explain any four methods of collecting primary data.
- Draw a histogram and frequency polygon for the following data.

Variable | Frequency | Variable | Frequency |

100-110 | 11 | 140-150 | 33 |

110-120 | 28 | 150-160 | 20 |

120-130 | 36 | 160-170 | 8 |

130-140 | 49 |

Also determine the value of mode from the histogram.

- Calculate arithmetic mean, median and mode from the following

frequency distribution.

Variable | Frequency | variable | Frequency |

10-13 | 8 | 25-28 | 54 |

13-16 | 15 | 28-31 | 36 |

16-19 | 27 | 31-34 | 18 |

19-22 | 51 | 34-37 | 9 |

22-25 | 75 | 37-40 | 7 |

- The number of workers employed, the mean wages (in Rs.) per month and standard deviation (in Rs.) in each section of a factory are given below. Calculate the mean wages and standard deviation of all the workers taken together.

Section | No. of workers
employed |
Mean Wages
(in Rs.) |
Standard deviation
(in Rs.) |

A | 50 | 1113 | 60 |

B | 60 | 1120 | 70 |

C | 90 | 1115 | 80 |

- Calculate Bowley’s coefficient of skewness from the following data.

Variable | frequency |

0-10 | 12 |

10-20 | 16 |

20 -30 | 26 |

30- 40 | 38 |

40 -50 | 22 |

50-60 | 15 |

60- 70 | 7 |

70 -80 | 4 |

- Calculate Karl Person’s coefficient of correlation from the following data.

X | 44 | 46 | 46 | 48 | 52 | 54 | 54 | 56 | 60 | 60 |

Y | 36 | 40 | 42 | 40 | 42 | 44 | 46 | 48 | 50 | 52 |

- Explain the concept of regression with an example.
- The sales of a company for the years 1990 to 1996 are given below:

Year | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 |

Sales (in lakhs of rupees) | 32 | 47 | 65 | 88 | 132 | 190 | 275 |

Fit an equation of the from Y = ab^{X }for the above data and estimate the

sales for the year 1997.

**SECTION ****–**** C**

*Answer any TWO questions*. (2 ´ 20 = 40 Marks)

- a) Explain (i) Judgement sampling (ii) Quota sampling and

(iii) Systematic sampling methods with examples.

- (i) Draw a blank table to show the distribution of personnel in a

manufacturing concern according to :

- Sex: Males and Females.
- Salary grade: Below Rs.5,000; Rs.5,000 -10,000;

Rs.10,000 and above.

- Years: 1999 and 2000
- Age groups: Below 25, 25 and under 40, 40 and above

(ii) Draw a multiple bar diagram for the following data:

Year | Sales (in’000Rs.) | Gross Profit | Net profit |

1992 | 120 | 40 | 20 |

1993 | 135 | 45 | 30 |

1994 | 140 | 55 | 35 |

1995 | 150 | 60 | 40 |

(10+5+5)

- a) (i) An incomplete distribution is given below

Variable | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

Frequency | 10 | 20 | f_{1} |
40 | f_{2} |
25 | 15 |

##### Given the median value is 35 and the total frequency is 170, find

the missing frequencies f_{1} and f_{2.}

- Calculate the value of mode for the following data:

Marks | 10 | 15 | 20 | 25 | 30 | 35 | 40 |

Frequency | 8 | 12 | 36 | 35 | 28 | 18 | 9 |

- b) Explain any two measures of dispersion. (7+7+6)
- a) The scores of two batsman A and B is 10 innings during a certain season are:

A | 32 | 28 | 47 | 63 | 71 | 39 | 10 | 60 | 96 | 14 |

B | 19 | 31 | 48 | 53 | 67 | 90 | 10 | 62 | 40 | 80 |

Find which of the two batsmen is consistent in scoring.

- Calculate the first four central moments and coefficient of skewness from the

following distribution.

Variable | frequency | Variable | Frequency |

25-30 | 2 | 45-50 | 25 |

30-35 | 8 | 50-55 | 16 |

35-40 | 18 | 55-60 | 7 |

40-45 | 27 | 60-65 | 2 |

(10+10)

- a) From the following data obtain the two regression equations and calculate

the correlation coefficient.

X | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |

Y | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |

- b) (i) Explain the concept of Kurtosis.

(ii) In a co-educational institution, out of 200 students 150 were boys.

They took an examination and it was found that 120 passed, 10 girls

had failed. Is there any association between gender and success in the

examination? (10+5+5)