Grouped Frequency Table

Q.

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class
$\begin{array}{cccccc}Marks& Below20& Below40& Below60& Below80& Below100\\ Numberofstudents& 17& 22& 29& 37& 50\end{array}$
Form the frequency distribution table for the data.

Q. Given below is a cumulative frequency distribution table. Corresponding to it, make an ordinary frequency distribution table.
$\begin{array}{cc}\text{x}& \text{cf}\\ \text{More than or equal to 0}& 45\\ \text{More than or equal to 10}& 38\\ \text{More than or equal to 20}& 29\\ \text{More than or equal to 30}& 17\\ \text{More than or equal to 40}& 11\\ \text{More than or equal to 50}& 6\end{array}$

Q. The difference between the upper class limit and lower class limit is called class .

1. width
2. frequency
3. interval
4. mark

Q.

Given below is the pulse count of 40 patients.

66, 79, 89, 67, 72, 82, 85, 80, 82, 81, 67, 87, 71, 68, 63, 74, 73, 86, 84, 75, 85, 80, 85, 61, 75, 85, 80, 85, 61, 75, 68, 69, 64, 75, 73, 72, 82, 76, 74, 77.
Group the data first in discontinuous class intervals such that one of the class intervals is 70-74.
Next, group the data in continuous class intervals such that one of the class intervals is 85-90.
Find the second class interval and the corresponding frequency of the class for both the groupings of the data.

1. 64-69, 6, 65-70, 6

2. 65-69, 6, 65-70, 6

3. 65-69, 6, 65-70, 7

4. 65-70, 6, 65-70, 6

Q. In a retail market , fruit vendors were selling mangoes kept in packed boxes. These boxes contained different number of mangoes. The following was the distribution of mangoes according to the number of boxes ?

Number of mangoes	$50-52$	$53-55$	$56-58$	$59-61$	$62-64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

Q.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$

The number of batteries having a life of 3.5-4.0 years is:
(Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5)

1. 4

2. 11

3. 6

4. 14

Q.

Range gives us an idea of how the data is dispersed about the central tendency.

1. True

2. False

Q.

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

1. All of the above

2. $\begin{array}{cc}\text{Marks}& \text{Number of students}\\ \text{0-10}& 17\\ \text{10-20}& 5\\ \text{20-30}& 7\\ \text{30-40}& 8\\ \text{40-50}& 13\\ \text{50-60}& 10\end{array}$

3. $\begin{array}{cc}\text{Marks}& \text{Number of students}\\ \text{0-10}& 7\\ \text{10-20}& 22\\ \text{20-30}& 29\\ \text{30-40}& 37\\ \text{40-50}& 50\\ \text{50-60}& 60\end{array}$

4. $\begin{array}{cc}\text{Marks}& \text{Number of students}\\ \text{0-10}& 17\\ \text{10-20}& 15\\ \text{20-30}& 7\\ \text{30-40}& 0\\ \text{40-50}& 13\\ \text{50-60}& 10\end{array}$

Q.

Observe the following table and answer which blood group is rarest?

Blood Group	Number of students
$\mathrm{A}$	$10$
$\mathrm{B}$	$8$
$\mathrm{O}$	$12$
$\mathrm{AB}$	$15$

Q.

The following data gives the marks obtained by students in an exam.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ Below10& 5\\ Below20& 10\\ Below30& 23\\ Below40& 31\\ Below50& 45\\ Below60& 49\end{array}$

(i)Convert the cumulative distribution to a regular distribution.

(ii)Calculate the mode. [3 MARKS]

Q. $\sqrt{1-\frac{x}{169}}=\frac{12}{13}$ find x.

Q. Find the sum of the cubes of first five natural numbers. Verify your answer by using formula $\left(n\right)(n+1)/2{]}^2$, where $n$ is a natural numbers. Also find the sum of the cubs of the first ten natural numbers.

Q.

The small groups obtained on dividing all the observations are called ________ and the size is called _________.

1. Class size, Class Interval
2. Class Interval, Class Size
3. Mid value, Range
4. Range, Mid Value

Q. The following box plots show how many hours fifth-grade students and seventh-grade students studied in a given month.


If their interquatile range are $I_1$ and $I_2$ respectively, then

1. $I_1>I_2$
2. $I_1<I_2$
3. $I_1=I_2$
4. None of the above

Q. Factorise the following:
${(a-3b)}^3+{(3b-c)}^3+{(c-a)}^3$

Q.

From the given table, find the rarest blood group.

$\begin{array}{cc}\text{Blood Group}& \text{Frequency}\\ \text{AB}& 6\\ \text{A}& 5\\ \text{B}& 3\\ \text{O}& 1\\ \text{Total}& 15\end{array}$

1. A

2. AB

3. O

4. B

Q.

The following table shows data during a 1hr exam for a student.

$$\begin{array}{cc}\text{Time during exam(mins)}& \text{Total number of questions solved in the exam}\\ 0-10& 2\\ 10-20& 5\\ 20-30& 10\\ 30-40& 15\\ 40-50& 17\\ 50-60& 25\end{array}$$

The number of questions completed by the student in the last 10 minutes of the examination is ?

1. 

2. 

3. 

4. 

Q. Explain the methods of calculating median?

Q. Divide $4x^4-3x^3-2x^2+6x-7$ by $x-2$.

Q.

Divide $(3x^2-x^3-3x+5)$ by $(x-1-x^2)$

Q. Find the $\sqrt{(1+\frac{27}{169})}=(1+\frac{x}{13})$

Q. The weekly wages (in rupees) of $28$ workers of a factory are given below:
$668,610,642,658,668,620,719,720,700,690,710,642,672,654,692,706,718,702,704,678,615,640,680,716,705,615,636,656.$
Construct a frequency table with equal class intervals, taking the first of the class intervals as $610-630,$ where $630$ is not included.

Q.

Question 14(i)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$

Construct a cumulative frequency table.

Q. Which of the following is not a sector of a circle?

1. Apple pie
2. Cathedral window
3. Pizza slice
4. Birthday cap

Q.

For discontinuous grouped data, the class interval is given in _______ form.

1. inclusive

2. exclusive

3. class-mark

4. frequency