1. Calculate the mean and mode of:
Central size 15 25 35 45 55 65 75 85
Frequencies 5 9 13 21 20 15 8 3
The following data shows the monthly expenditure of 80 students of a university on morning food.
Exp in $

No of Students

$

No. of Student

78  82

2

5357

13

73  77

6

4853

9

68  72

7

43  47

7

63  67

12

48  42

4

58  62

18

33  37

2

Calculate mean, SD & Coefficient of variation.
Calculate Karl Pearson's Coefficient of correlation between values of X & Y given below. Calculate the probable error.
X

78

89

96

69

59

79

68

61

Y

125

96

156

112

107

136

123

108

A project scheduling the following characteristics
Activity 12 13 24 34 35 49 56 57 68 78 810 910
Time (days)
4 1 1 1 6 5 4 8 1 2 5 7
Summarize the CPM calculations in a tabular form and determine the critical path.
In a car manufacturing plant, a loading crane takes exactly 10 minutes to load a car into a wagon and again come back to the position of loading another car. If the arrivals of cars is a Poisson stream at an average of one every 20 minutes. Calculate the average waiting time of a car.
The ranks of the same 15 students in two subjects A and B are given below, the two numbers within the brackets denoting the ranks of the same student in A and B respectively:
(1, 10), (2, 7), (3, 2), (4, 6), (5, 4), (6, 8), (7, 3), (8, 1), (9, 11), (10, 15), (11, 9), (11, 5), (13, 14), (14, 12), (15, 13)
Use Spearman's formula to find the rank correlation coefficient.