Exercise 9.1

1. Write the mark wise frequencies in the following frequency distribution table.

Solution:

To Find Mark-wise frequencies:

Solution:

Marks 5: students

Marks 6: 11 - 5 = students

Marks 7: 19 - 11 = students

Marks 8: 31 - 19 = students

Marks 9: 40 - 31 = students

Marks 10: 45 - 40 = students

Frequency Distribution Table:

2. The blood groups of 36 students of IX class are recorded as follows.

A O A O A B O A B A B O

B O B O O A B O B AB O A

O O O A AB O A B O A O B

Represent the data in the form of a frequency distribution table. Which is the most common and which is the rarest blood group among these students?

Solution:

Given:

Blood group data with frequencies.

Frequency Distribution Table:

Most Common Blood Group:

(with a frequency of 15)

Most Rarest Blood Group:

(with a frequency of 2)

3. Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows;

1 2 3 2 3 1 1 1 0 3 2 1

2 2 1 1 2 3 2 0 3 0 1 2

3 2 2 3 1 1

Prepare a frequency distribution table for the data given above.

Solution:

Given:

Number of heads in 30 tosses of three coins.

To Find Frequency distribution table:

Solution:

Let's count the occurrences of 0, 1, 2, and 3 heads:

0 Heads:

1 Head:

2 Heads:

3 Heads:

Frequency Distribution Table:

4. A TV channel organized a SMS(Short Message Service) poll on prohibition on smoking, giving options like A-complete prohibition, B-prohibition in public places only, C-not necessary. SMS results in one hour were

A B A B C B

A B B A C C B B A B

B A B C B A B C B A

B B A B B C B A B A

B C B B A B C B B A

B B A B B A B C B A

B B A B C A B B A

Represent the above data as grouped frequency distribution table. How many appropriate answers were received? What was the majority of peoples' opinion? 20

Solution:

Given:

SMS poll results: A (Complete prohibition), B (Prohibition in public places only), C (Not necessary).

To Find Grouped frequency distribution table, total responses, and majority opinion:

Solution:

Let's count the occurrences of A, B, and C:

A:

B:

C:

Grouped Frequency Distribution Table:

Total Appropriate Answers Received: 20 + 36 + 14 =

Majority Opinion: BA (Prohibition in public places only)

5. Represent the data in the adjacent bar graph as a frequency distribution table.

Solution:

Frequency Distribution Table:

6. Identify the scale used on the axes of the adjacent graph. Write the frequency distribution from it.

Solution:

Given:

Scale on X-axis: 1 cm = 1 class interval Scale on Y-axis: 1 cm = 10 number of students

Frequency Distribution Table:

7. The marks of 30 students of a class, obtained in a test (out of 75), are given below... Form a frequency table with equal class intervals. (Hint: one of them being 0-10).

42, 21, 50, 37, 42, 37, 38, 42, 49, 52, 38, 53, 57, 47, 29,

59, 61, 33, 17, 17, 39, 44, 42, 39, 14, 7, 27, 19, 54, 51.

Solution:

Frequency Distribution Table:

8. The electricity bills (in rupees) of 25 houses in a locality are given below. Construct a grouped frequency distribution table with a class size of 75.

170, 212, 252, 225, 310, 712, 412, 425, 322, 325, 192, 198, 230, 320,

412, 530, 602, 724, 370, 402, 317, 403, 405, 372, 413.

Solution:

Given:

Class size is

Frequency Distribution Table:

9. A company manufactures car batteries of a particular type. The life (in years) of 40 batteries were recorded as follows... Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2-2.5.

2.6, 3.0, 3.7, 3.2, 2.2, 4.1, 3.5, 4.5,

3.5, 2.3, 3.2, 3.4, 3.8, 3.2, 4.6, 3.7,

2.5, 4.4, 3.4, 3.3, 2.9, 3.0, 4.3, 2.8,

3.5, 3.2, 3.9, 3.2, 3.2, 3.1, 3.7, 3.4,

4.6, 3.8, 3.2, 2.6, 3.5, 4.2, 2.9, 3.6.

Solution:

Class size = starting from 2 – 2.5

Frequency Distribution Table: