Problem set IV UC 207

Due date: 21-3-14

1. How many numbers of significant figures does each of the following numbers have?

0.216, 90.7, 800.0, 0.0670, 0.092067, 5.06250, 123000, 1.23× 105

2. Find out the value for the following operation (answer should be rounded off to correct

significant figure)

7.987 m - 0.54 m, 3.12 g + 0.8 g + 1.033 g , 140 cm × 35 cm, 35 000 kJ ÷ 0.250 min

3. What will be the value for the following set of logarithms (answer should be rounded off

to correct significant figure)

log(3.000x104), log(3x104), pH of 1.8×10-4 M aqueous HCl solution , log(2.73×10-5 )

4. What will be the correct way of representing the result of the following mathematical

expression (answer should be rounded off to correct significant figure)

a). (1.3 x 103)(5.724 x 104)

b). ((5.254+0.0016)/34.6) - 2.231×10-3

5. What is the standard deviation of the first 10 natural numbers (1 to 10)?

6. Two students analysed sample of gold and obtained following results:

A-set: 107.861, 107.870, 107.881, 107.892

B-set: 107.777, 107.778, 107.779, 107.780

Calculate the mean and standard deviation in both set of values?

7. Ten friends scored the following marks in their end-of-year math exam:

23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%, 72% and 82%

What was the standard deviation and variance of their marks?

8. Ramiro did a survey of the number of pets owned by his classmates, with the following results:

What was the standard deviation?

9. Consider the following three data sets A, B and C. A = {9,10,11,7,13} B = {10,10,10,10,10} Find C = {1,1,10,19,19} a) Calculate the mean of each data set. b) Calculate the standard deviation of each data set. c) Which set has the largest standard deviation? d) Is it possible to answer question c) without calculations of the standard deviation?

10. The following table shows the grouped data, in classes, for the heights of 50 people.

height (in cm) - classes frequency 120 - 130 2 130 - 140 5 140 - 150 25 150 - 160 10 160 - 170 8

a) Calculate the mean of the height of the people. b) Calculate the standard deviation from the above table.