SOLVE FOR THE FOLLOWING PROBLEMS AND SHOW SOLUTIONS IN PROPER FORMAT.
1. Given the data set
4, 10, 7, 7, 6, 9, 3, 8, 9
Find
a) the mode,
b) the median,
c) the mean,
d) the sample standard deviation.
e) If we replace the data value 6 in the data set above by 24, will the standard deviation
increase, decrease or stay the same?
2. A student's marks in five tests are 36%, 78%, 67%, 88% and 98%. The weights for the five tests
are 1, 2, 2, 3, 3 respectively. Find the weighted mean $\mu$ of the five tests.
3. Find the mean of the following data
Marks Below 10 10-30 30-60 60-100 100-150 Above 150
No. of
Students 4 7 10 16 8 2
4. The following are the monthly salaries in '000 of 20 employees in a firm:
130 62 145 118 125 76 151 142
110 98 65 116 100 103 71 85
80 122 132 95
The firm gave bonus of 10, 15, 20, 25 and 30 to the individual in the respective salary groups
exceeding 60 but not exceeding 80, exceeding 80 but not exceeding 100, and so on up to
exceeding 140 but not exceeding 160.
Find:
a. The total bonus paid
b. Average bonus paid per employee
