Grouped Frequency Table

Q.

If x⁴+1/x⁴=119, find the value of x³-1/x³

Q.

Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16.

Q.

The marks obtained by 40 students of a class in an examination are given below.
3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 24, 6, 23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 10-15 (15 not included).

Q.

The heights (in cm) of 30 students of a class are given below:
161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148, 153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152, 147, 155, 155, 157.
Prepare a frequency table as well as a cumulative frequency table with 160-165 (165 not included) as one of the class intervals.

Q.

Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

Q.

Q.

Construct a frequency table with equal class intervals from the following data on the daily wages (in Rs.) of 28 labourers workiing in a factory, taking one of the class intervals as 210-230 (230 not included) .
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

Q. In the tables given below, class-mark and frequencies is given. Construct the frequency tables taking inclusive and exclusive classes.

(i)

Class width	Frequency
5	3
15	9
25	15
35	13

(ii)

Class width	Frequency
22	6
24	7
26	13
28	4

Q. Question 3
Factorise the following using appropriate identities:
(i) $9x^2+6xy+y^2$
(ii) $4y^2-4y+1$
(iii) $x^2-\frac{y^2}{100}$

Q.

The weights (in grams) of 40 oranges picked at random from a basket are as follows:
40, 50, 60, 65, 45, 55, 30, 90, 75, 85, 70, 85, 75, 80, 100 110, 70, 55, 30, 35, 45, 70, 80, 85, 95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 45, 84.
Construct a frequency table as well as a cumulative frequency table.

Q. Factorise each of the following:
(i) $8a^3+b^3+12a^b+6a{b}^2$
(ii) $8a^3-b^3-12a^{2}b+6a{b}^2$
(iii) $27-125a^3-135a+225a^2$
(iv) $64a^3-27b^3-144a^{2}b+108a{b}^2$
(v) $27p^3-\frac{1}{216}-\frac{9}{2}{p}^2+\frac{1}{4}p$

Q.

Given below is a cumulative frequency table:
$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ \text{Below}10& 17\\ \text{Below}20& 22\\ \text{Below}30& 29\\ \text{Below}40& 37\\ \text{Below}50& 50\\ \text{Below}60& 60\end{array}$
Extaract a frequency table from the above.

Q.

Question 15
In the figure, there is a histogram depicting daily wages of workers in a factory. Construct the frequency table.

Q. Question 9
A grouped frequency distribution table with classes of equal sizes using 63 - 72 (72 included) as one of the class is constructed for the following data.

30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88

40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96

102, 110, 88, 74, 112, 14, 34, 44.
The number of classes in the distribution will be:

A) 9
B) 10
C) 11
D) ​​​​​​​12

Q.

Q.

Present the following as an ordinary grouped frequency table:
$\begin{array}{ccccccc}\text{Marks (below)}& 10& 20& 30& 40& 50& 60\\ \text{(Number of students)}& 5& 12& 32& 40& 45& 48\end{array}$

Q.

Question 44

Four times a number is a ___ % increase in the number.

Q.

if x>0 and x^2+1/9x^2 =25/36, find:x^3+1/27x^3.

Q. Salaries of 30 people are represented in the grouped frequency distribution table given below.

Salary (In Rupees)	Number of people
5000-10000	5
10000-20000	10
20000-30000	15

How many people salary lie in between ₹10000 to ₹30000?

1. 5
2. 10
3. 15
4. 25

Q.

If 2x+3y=13 and xy=6 find the value of 8x³+27y³.

Q.

The number of books in different shelves of a library are as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45,

16, 20 19, 24, 27, 30, 32, 34, 35, 42,

27, 28, 19, 34, 38, 39, 42, 29, 24, 27,

22, 29, 31, 19, 27, 25, 28, 23, 24, 32,

34, 18, 27, 25, 37, 31, 24, 23, 43, 32,

28, 31, 24, 23, 26, 36, 32, 29, 28, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

Q.

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:
$\begin{array}{ccccccc}\text{Age (in years)}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Numbr of patients}& 90& 50& 60& 80& 50& 30\end{array}$
Construct the cumulative frequency table for the above data.

Q. Factorise each of the following:
(i) $27y^3+125z^3$
(ii) $64m^3-343n^3$

Q.

Thirty children were asked about the number of hours they watched T.V. programmes in the previous week. The results were found as follows:
1 6 2 3 5 12 5 8 4 8
10 3 4 12 2 8 15 1 17 6
3 2 8 5 9 6 8 7 14 12
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10
(ii) How many children watched television for 15 or more hours a week?

Q. The daily minimum temperatures in degrees Celsius recorded in a certain Arctic region are as follows:

− 12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, −2.4, 0, 3.2, 2.7, 3.4, 0, −2.4, −2.4, 0, 3.2, 2.7, 3.4, 0, −2.4, −5.8, −8.9, −14.6, −12.3, −11.5, −7.8, −2.9.

Represent them as frequency distribution table taking −19.9 to − 15 as the first class interval.

Q.

The following are the marks (out of 25) obtained by 20 students in a class test :

18, 21, 15, 23, 5, 7, 12, 8, 12, 18, 25, 18, 21, 15, 23, 18, 25, 5, 7, 23

Write the above data in the form of table using tally marks and answer the following questions:
How many students got marks above 20?

Q.

Question 155

As per the census of 2001, the population of four states are given below

$\begin{array}{cccc}& \left(a\right)& Maharashtra& 96878627\\ & \left(b\right)& AndhraPradesh& 76210007\\ & \left(c\right)& Bihar& 82998509\\ & \left(d\right)& UttarPradesh& 166197921\end{array}$

Arrange the states in ascending and descending order of their populations.

Q.

12(x^{​​​​​​2}​​​+7)²-8(x^{​​​​​​2}​​​​​+7)²(2x-1)-15(2x-1)²

Q. Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included):

220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

Q. Find the mean of the following distribution:

x:	10	12	20	25	35
f:	3	10	15	7	5