St. Xavier’s College (Autonomous)
B. Com – BPS Semester – 1
Assignment
Business Statistics (1102)
Unit 1, 2 and 5

Q – 1: Calculate Karl Pearson’s correlation coefficient for the given data. X | 0.05 | 0.14 | 0.24 | 0.30 | 0.47 | 0.52 | 0.57 | 0.61 | 0.67 | 0.72 | Y | 1.08 | 1.15 | 1.27 | 1.33 | 1.41 | 1.46 | 1.54 | 2.72 | 4.01 | 9.63 |

Q – 2: Calculate Spearman’s correlation coefficient for the given data. X | 612 | 524 | 594 | 592 | 524 | 621 | 524 | 800 | 524 | 900 | 621 | Y | 3.1 | 4.2 | 4.2 | 4.2 | 5 | 6 | 4.2 | 9.5 | 6.2 | 10 | 3 |

Q – 3: The following table gives, according to age the frequency of marks obtained by 100 students in an intelligence test. Calculate the correlation coefficient. Marks | Age (in years) | | 18 | 19 | 20 | 21 | 60 – 70 | – | 2 | 3 | 1 | 50 – 60 | – | 2 | 4 | 4 | 40 – 50 | 4 | 4 | 6 | 8 | 30 – 40 | 6 | 8 | 10 | 11 | 20 – 30 | 5 | 4 | 6 | 4 | 10 – 20 | 4 | 2 | 2 | – |

Q – 4: The following data are obtained for two variables x and y. n = 30, ∑x = 120, ∑y = 90, ∑xy = 356, ∑x2 = 600, ∑y2 = 250
Later on it was observed that two pairs were wrongly taken as (8, 10) and (12, 7) instead of (8, 12) & (10,8). Find the correct value of the correlation coefficient.

Q – 5: Find the coefficient of correlation from the following data: n = 20, ∑x = 550, ∑y = 400, ∑(x – 25)2 = 305, ∑(y – 20)2 = 320, ∑(x – 25)(y – 20) = 60.

Q – 6: From a sample of 1000 persons of a town, the following information is obtained.
550 persons were not inoculated against cholera. The proportion of persons not affected by cholera and affected by cholera was 7:3. 350 persons were not inoculated though they were not attacked by cholera. Examine whether inoculation is effective in preventing cholera.

Q – 7:1000 students were appeared in an examination. The number of boys were 20% more than the number of girls. The number of failed students were 166 less than the number of passed students, and 58 girls were failed in and examination. Find Yule’s coefficient of association.

Q – 8: Find the association between post graduate students and their presence in the library. Class | FY | SY | TY | M. Com. 1 | M. Com. II | No. of students | 250 | 200 | 175 | 50 | 40 | No. of students present in a library | 50 | 40 | 50 | 20 | 15 |

Q- 9 If verify that (i) (A+B)T = AT + BT (ii) (AB)T = BTAT.

Q-10 If and (A+B)2 = A2 + B2, find x and y.

Q-11 If find the value of x.

Q-12 Solve the following linear equation by matrix method.

Q-13 If is a symmetric matrix find a, b and c, also find a matrix B such that A +2B = I. where I is a unit matrix.

Q-14 If; find the values of x and y such that AB = BA.

Q-15 A person buys 2 pineapples, 3 mangoes and 4 apples in Rs.43. Another person buys 1 pineapple, 4 mangoes and 2 apples in Rs. 34. And a third person buys 5 pineapple, 2 mangos and 3 apples in Rs. 66. Find the price of each fruit using inverse of a matrix.