Grouped Frequency Distribution

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Q. Question 1
The following are the marks (out of 100) of 60 students in Mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35,
72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55,
26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class starting from 0 - 9.

Q.

Question 14

In a frequency distribution with classes 0-10, 10-20 etc., the size of the class intervals is 10. The lower limit of fourth class is:

(a) 40

(b) 50

(c) 20

(d) 30

Q.

Construct a frequency table with class-intervals 0-5 (5 not included) of the following marks obtained by a group of 30 students in an examination:

0, 5, 7, 10, 12, 15, 20, 22, 25, 27, 8, 11, 17, 3, 6, 9, 17, 19, 21, 29, 31, 35, 37, 40, 42, 45, 49, 4, 50, 16.

Q.

The marks scored by 20 students in a test are given below: 54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57 Complete the following frequency table:

$\begin{array}{ccc}\text{Marks in class intervals}& \text{Tally marks}& \text{Frequency (No.of children)}\\ 40-50& & \\ 50-60& & \\ 60-70& & \\ 70-80& & \\ 80-90& & \end{array}$

What is the class interval in which the greatest frequency occurs?

Q. If $\frac{2}{5x}-\frac{5}{3x}=\frac{1}{15}$, then the value of '$x$' is

1. - 19
2. 39
3. 43
4. 19

Q.

The difference between the upper and lower limit of a class interval is called the ______ of the class interval.

Q.

Construct a frequency distribution table for the following marks obtained by 25 students in a history test in calss VIII of a school :

9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9, 12, 17, 19, 19, 20, 9

(i) What is the range of marks ?

(ii) What is the highest mark ?

(iii) Which mark is occurring more frequently ?

Q.

In the class interval $20–30$, the lower class limit is ____

Q.

Question 100(i)

Construct a frequency distribution table for the following weights (in grams) of 35 mangoes, using the equal class intervals, one of them is 40-45 (45 not included):
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37,
53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68
How many classes are there in the frequency distribution table ?

Q.

The marks obtained by 40 students of a class in an examination are given below :

8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34 Prepare a frequency distribution table with equal class invtervals starting from 0 - 10 (where 10 is not included).

Q.

The marks obtained by 40 students of class VIII in an examination are given below:

16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12, 6, 8; 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.

Divide the data into five groups, namely 0-5, 5-10, 10-16, 15-20 and 20-25 and prepare a grouped frequency table.

Q.

Question 30

Upper limit of class interval 75 - 85 is
(a) 10
(b) -10
(c) 75
(d) 85

Q.

Sum of two number is 42. One number is 6 more than the other number .What are the numbers?

Q.

The weekly pocket expenses (in rupees) of 30 students of a class are given below :

62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 87, 85, 105, 115.

Construct a frequency table with class intervals 60 - 70 (where 70 is not included), 70 - 80, 80 - 90, etc.

Q.

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

___

Q.

The electricity bills (in rupees) of 25 houses of a cetrain locality for a month are given below :

324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472.

Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300 - 400, where 400 is not included.

Q.

What is the lower class limit for the class interval 40 - 70?

1. 55

2. 40

3. 45

4. 35

Q.

The marks awarded for an assignment for a class of 20 students were as follows:
6 7 5 7 7 8 7 6 9 7
4 10 6 8 8 9 5 6 4 8

The frequency table for this data is:

1. $\begin{array}{cc}Marksobtained& Frequency\\ 04& 2\\ 05& 2\\ 06& 4\\ 07& 5\\ 08& 4\\ 09& 2\\ 10& 4\end{array}$

2. $\begin{array}{cc}Marksobtained& Frequency\\ 04& 1\\ 05& 2\\ 06& 4\\ 07& 5\\ 08& 4\\ 09& 2\\ 10& 1\end{array}$

3. $\begin{array}{cc}Marksobtained& Frequency\\ 04& 2\\ 05& 2\\ 06& 4\\ 07& 5\\ 08& 4\\ 09& 3\\ 10& 1\end{array}$

4. $\begin{array}{cc}Marksobtained& Frequency\\ 04& 2\\ 05& 2\\ 06& 4\\ 07& 5\\ 08& 4\\ 09& 2\\ 10& 1\end{array}$

Q.

In a frequency distribution, the first and the second class intervals are 0 -10 and 10 -20. Then, the lower limit of the fourth class interval is

1. 30
2. 50
3. 20
4. 40

Q.

Question 91

Following are the numbers of members in 25 families of a village :6, 8, 7, 7, 6, 5, 3, 2, 5, 6, 8, 7, 7, 4, 3, 6, 6, 6, 7, 5, 4, 3, 3, 2, 5 Prepare a frequency distribution table for the data using class intervals 0-2, 2-4 etc.

Q.

Question 38

In the class interval 26-33, 33 is known as ___.

Q. Find the common factors of the given terms.
(i) $12x,36$

Q.

Question 58

In the class intervals 10-20 and 20-30 respectively, 20 lies in the class___.

Q.

The age of 15 students in a class is given below:

10, 11, 12, 10, 10, 12, 13, 13, 11, 10, 12, 11, 12, 13, 10

Find the frequency of age 13.

1. 2

2. 3

3. 1

4. 1

Q.

The daily earnings (in rupees) of 24 stores in a market was recorded as under :

715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700.

Prepare a frequency table taking equal class - sizes. One such class is 500 - 550, where 550 is not included.

Q. The optimum temperature required by the seeds for germination is:

1. 15${}^o$C- 25${}^o$C
2. 25${}^o$C- 35${}^o$C
3. 35${}^o$C- 45${}^o$C
4. 45${}^o$C- 55${}^o$C

Q.

Use the frequency distribution shown below to construct an expanded frequency distribution high temperatures (F).

Class	$20-30$	$31-41$	$42-52$	$53-63$	$64-74$	$75-85$	$86-96$
Frequency	$17$	$41$	$67$	$68$	$79$	$67$	$26$

Q.

Arrange the heights of 20 students in a grouped distribution table with a class interval of 5. The number of students whose height is below 165cm is ___

Heights (in cm): 150, 153, 162, 170, 186, 153, 162, 180, 165, 150, 178, 156, 184, 176, 173, 186, 159, 183, 180, 156.

Q.

Question 82(iii)

Given below is a frequency distribution table. Read it and answer the questions that follow.
$\begin{array}{cc}Classinterval& Frequency\\ 10-20& 5\\ 20-30& 10\\ 30-40& 4\\ 40-50& 15\\ 50-60& 12\end{array}$
What is the frequency of the third class ?