## Business Mathematics and Statistics – University Past Papers.

Q. (a) Calculate the median, the upper and lower quartiles from the following data:

Class Intervals | Under 25 | 25-29 | 30-34 | 35-39 | 40-44 | 45-49 | 50-54 | 55-59 | 60 and over |

Frequency | 222 | 405 | 508 | 520 | 525 | 490 | 457 | 416 | 166 |

(b) Calculate the mean deviation from (i) the mean, (ii) the median, of the following set of examination marks: 45, 32, 37, 46, 39, 36, 41, 48 and 36. Calculate the coefficient

of mean deviation.

Q. (a) A man invites 5 friends. He was born in April as also all the invited friends.

What is the probability that none of the friends was born on the same day of the

month as the host.

(b) Find the value of k so that the function f(x) defined as follows, maybe a density function. Also, compute the distribution function F(x).

Q. (a) If X is binomially distributed with mean 3.20 and variance 1.152, find the complete

binomial probability distribution.

(b) The probability that a man aged 50 years will die within a year is 0.01125. What

is the probability that of 12 such men at east 11 will reach their fifty-first

birthday?

Q. (a) Compute the least squares regression equation of Y on X for the following data.

What is the regression coefficient and what does it mean?

X | 5 | 6 | 8 | 10 | 12 | 13 | 15 | 16 | 17 |

Y | 16 | 19 | 23 | 28 | 36 | 41 | 44 | 45 | 50 |

(b) Fit a second degree trend curve to the following data and compute the trend

values.

Year | 1931 | 1933 | 1935 | 1937 | 1939 | 1941 | 1943 | 1945 |

Index of wholesale prices | 96 | 87 | 91 | 102 | 108 | 139 | 307 | 289 |

#### Q. (a) Find the equation of the line that passes through the points (–2, 4) and (1, 2).

(b) Find the equation of line with slope 6 passes through the point (3, 5).

Q. (a) The following distribution shows Kilowatt Hours of electricity used in one

month by 75 residential consumers in a certain locality of Lahore.

Consumption in kilowatt hours | 5-24 | 25-44 | 45-64 | 65-84 | 85-104 | 105-121 | 125-144 | 145-161 |

No. of consumers | 4 | 6 | 14 | 22 | 14 | 5 | 7 | 3 |

Estimate the mean, the median and the two quartiles.

(b) Calculate the variance and standard deviation of the following marks obtained by 9

students: 45, 32, 46, 39, 36, 41, 48, 36.

Q. (a) A box contains six discs numbered 1 to 6. Find for each integer k from 3 to 11, the

probability that the numbers on two discs drawn without replacement have sum equal

to k.

**Q. (a)**Write the slope-intercept form of the equation of the line with slope 3, and which

passes through the point (1, −4).

**(b)**Write the equation of the line that passes through (1, −6) and (−1, 2).

**Q. **Solve the following system of equations using Gaussian elimination.

**Q4. (a) **Given below are the marks obtained by 9 students: 45, 32, 37, 46, 39, 36, 31, 48 and

- Find the median and the quartiles.

** (b)**Calculate the mode for the distribution examination marks given in

Marks | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |

No. of Students | 8 | 87 | 190 | 304 | 211 | 85 | 20 |

** **

**Q. (a)**Calculate the variance and standard deviation from the following marks obtained by 9

students: 45, 32, 37, 46, 39, 36, 41, 48, 36.

**(b) **Goals scored by two teams A and B in a football season were as follows:

No. of goals scored in a match | Number of Matches | |

A | B | |

0 | 27 | 17 |

1 | 9 | 9 |

2 | 8 | 6 |

3 | 5 | 5 |

4 | 4 | 3 |

Find the coefficient of variation, find which team may be considered more consistent.

**Q. (a)**Following are the prices of a commodity for the years ending with 1957. Calculate the index numbers with **(i)** 1948 as base; and **(ii)** average of first five years as a base.

Year | 1948 | 1949 | 1950 | 1951 | 1952 | 1953 | 1954 | 1955 | 1956 |

Price in Rs. | 5.25 | 5.87 | 6.12 | 5.50 | 6.25 | 6.62 | 6.75 | 7.12 | 6.50 |

** **

**(b)**Six white balls and four black balls, which are indistinguishable apart from colour,

are placed in a bag. If six balls are taken from the bag, find the probability of their being three white and three black.

** **

**Q. (a) **Find the value of k so that the function f(x) defined as follows, may be a density function.

** **

**Q. **Given the following system of equations, find the value of x, y, z

**Q. (a) **Use the alternative formula for standard deviation to find the standard deviation of the following set

of numbers5, 6, 6, 7, 7, 8, 8, 8, 9, 10.

** (b)** Find the mean, median, and mode of the set of measurements 5, 12, 7, 14, 9, 7.

** **

**Q. (a)**Define Time series and briefly explain its four components?

**(b) **Find the first and third quartiles of the set {3, 7, 8, 5, 12, 14, 21, 15, 18, 14}.

** **

**Q. (a)**If X is a binomially distributed with mean 3.20 and variance 1.152, find the complete binomial

probability distribution.

**(b)**How does the correlation coefficient relate to the slope of the regression line?

** **

**Q. **The number of industrial injuries per working week in a particular factory is known to follow a Poisson

distribution with mean 1.5.

Find the probabbility that

- in a particular week there will be:

- less than 5 accidents,
- more than 5

- in a three week period there will be no accidents.