#### NATIONAL MANAGEMENT COLLEGE, THUDUPATHI

#### BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTIC

#### PRACTICE PROBLEMS

- Given the following data:

Cities | A | B | C | D | E | F |

Density | 200 | 500 | 400 | 700 | 600 | 300 |

Death rate | 10 | 16 | 14 | 20 | 17 | 13 |

Find the coefficient of correlation between density and death rate.

- For a Private data: {(x,y): (15,3),(11,3),(12,2),(14,0),(8,6)}. Find the coefficient of correlation between x and y.
- What is the value of correlation coefficient due to person on the basis of the following data:

X | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |

Y | 27 | 18 | 11 | 6 | 3 | 2 | 3 | 6 | 11 | 18 | 27 |

- Calculate Karl Pearson’s coefficient of correlation from the following data:

Values of X | 100 | 110 | 115 | 116 | 120 | 125 | 130 | 135 |

Values of Y | 18 | 18 | 17 | 16 | 16 | 15 | 13 | 10 |

- From the following data compute the coefficient of correlation between X and Y:

X – Series | Y – Series | |

Arithmetic Mean | 15 | 28 |

Sum of Squares of deviations from mean | 144 | 225 |

6) For the distribution of the number of marks obtained by 49 students in a class. Calculate the mean, median and mode.

Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 |

Frequency | 5 | 6 | 15 | 10 | 6 | 3 | 3 | 1 |

7) Calculate Q_{3}, D_{4}, P_{30 }from the following data:

Marks | 20 | 25 | 30 | 35 | 40 |

No.of students | 5 | 14 | 20 | 11 | 10 |

8) Find the A.M.G and H.M and prove that A.M ≥ G,M ≥ H.M

X | 2 | 4 | 8 | 16 |

F | 2 | 3 | 3 | 2 |

9) (i) If the absolute deviations of 5 observations from mean be 26, 15,39,24,41 Find the mean deviation about mean.

(ii) The first three quartiles of a distribution are Rs. 12, Rs.22, Rs.45; Find the Quartiles Deviation.

10) (i) If the standard deviation of x is, what is the variance of (5 – 2x)?

(ii) There are 5 bags of wheat weighting on an average 102kgs and another 8 bags weighting 98kgs on an Average. What is combined mean of 13 bags?

11) (i) What is the coefficient of range for the following wages of 8 workers? Rs.80, Rs.65, Rs.90, Rs.60, Rs. 75, Rs. 70, Rs. 72, Rs.85.

(ii) Calculate S.D for first 10 natural numbers.

12) (i) Calculate M.D and Q.D if S.D = 60

(ii) Calculate S.D and Q.D if M.D = 60. (ii) Calculate S.D and M.D if Q.D = 60; if the series are moderately asymmetrical.