Cumulative Frequency

Q.

Question 5
Convert the given frequency distribution into a continuous grouped frequency distribution.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 150-153& 7\\ 154-157& 7\\ 158-161& 15\\ 162-165& 10\\ 166-169& 5\\ 170-173& 6\end{array}$

In which intervals would 153.5 and 157.5 be included?

Q.

State True or False.
In a committee $50$ people speak French, $20$ speak Spanish, and $10$ speak both Spanish and French. The number of persons speaking at least one of these two languages is $60$.

1. $60$

2. $40$

Q.

Look at the cumulative frequency distribution table given below:

$\begin{array}{cc}Monthlyincome& Numberoffamilies\\ MorethanRs.10000& 100\\ MorethanRs.14000& 85\\ MorethanRs.18000& 69\\ MorethanRs.20000& 50\\ MorethanRs.25000& 37\\ MorethanRs.30000& 15\end{array}$

Number of families having income range 20000 to 25000 is

(a) 19 (b) 16 (c) 13 (d) 22

Q.

If the median of the following data is 50, then find the value of $p$.
$$\begin{array}{cc}\text{Class}& \text{Frequency}\\ \text{0 - 20}& 10\\ \text{20 - 40}& 7\\ \text{40 - 60}& 16\\ \text{60 - 80}& p\\ \text{80 - 100}& 8\end{array}$$

1. 7
2. 8
3. 9
4. 6

Q. Question 10
The following table shows the cumulative frequency distribution of marks of 800 students in an examination.
$\begin{array}{cc}Marks& Numberofstudents\\ Below10& 10\\ Below20& 50\\ Below30& 130\\ Below40& 270\\ Below50& 440\\ Below60& 570\\ Below70& 670\\ Below80& 740\\ Below90& 780\\ Below100& 800\end{array}$
Construct a frequency distribution table for the data above.

Q.

In a frequency distribution table with 12 classes, the class-width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?

Q.

(Use a graph paper for this question) The daily pocket expenses of 200 students in a school are given below: [4 MARKS]

Pocket expenses (in Rs.)	No.of students (frequency)
0-5	10
5-10	14
10-15	28
15-20	42
20-25	50
25-30	30
30-35	14
35-40	12

Draw a histogram representing the above distribution and estimate the mode from the graph.

Q. Cumulative frequency curve is also known as ogive.

1. False
2. True

Q.

The cumulative frequency table is useful in determining the

(a) mean (b) median

(c) mode (d) all of these

Q.

Draw a cumulative frequency curve (ogive) for each of the following distributions :

(i) $\begin{array}{ccccccc}Classinterval& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ Frequency& 10& 15& 17& 12& 10& 8\end{array}$

(ii) $\begin{array}{cccccc}Classinterval& 10-19& 20-29& 30-39& 40-49& 50-59\\ Frequency& 23& 16& 15& 20& 12\end{array}$

Q. The distribution below gives the weight of 30 students in a class. Find the median weight of students:

Weight (in kg):	40−45	45−50	50−55	55−60	60−65	65−70	70−75
No. of students:	2	3	8	6	6	3	2

Q.

The following are the marks obtained in Maths by students of Class 8:
51, 94, 34, 20, 50, 81, 81, 90, 76, 34, 51, 86, 93, 99, 26, 54, 85, 71, 88, 40, 44, 56, 55, 57, 78, 53, 81, 78, 65, 78.
The data have to be grouped to find the mean marks. One of the class intervals made is 60-70.

What is the frequency of the last class interval?

1. 2
2. 8
3. 5
4. 4

Q.

Find the mean, mode and median of the following data: [CBSE 2008]

Class	0−20	20−40	40−60	60−80	80−100	100−120	120−140
Frequency	6	8	10	12	6	5	3

Q. Question 8
For the following distribution,
$\begin{array}{cc}Marks& Numberofstudents\\ Below10& 3\\ Below20& 12\\ Below30& 27\\ Below40& 57\\ Below50& 75\\ Below60& 80\end{array}$
the modal class is
(a) 10 - 20
(b) 20 - 30
(c) 30 - 40
(d) 50 - 60

Q.

Use graph paper for this question.

The table given below shows the monthly wages of some factory workers.

(i) Using the table, calculate the cumalative frequencies of workers.

(ii) Draw a cumulative frequency curve.

Use 2 cm = Rs. 500, starting the origin at Rs. 6500 on x-axis, and 2 cm = 10 workers on thr y -axis.

$\begin{array}{cccccccc}\text{Wages (in Rs.)}& 6500-7000& 7000-7500& 7500-8000& 8000-8500& 8500-9000& 9000-9500& 9500-10000\\ \text{No. of workers}& 10& 18& 22& 25& 17& 10& 8\end{array}$

Q. Which one of the following measures is determined only after the construction of cumulative frequency distribution?

(a) Mean
(b) Median
(c) Mode
(d) None of these

Q. Draw an ogive by less than method for the following data:

No. of rooms:	1	2	3	4	5	6	7	8	9	10
No. of houses:	4	9	22	28	24	12	8	6	5	2

Q.

Find the mode, median and mean for the following data: [CBSE 2009]

Marks obtained	25−35	35−45	45−55	55−65	65−75	75−85
Number of students	7	31	33	17	11	1

Q.

Question 6
The expenditure of a family of different heads in a month is given below.

$\begin{array}{ccccccc}\text{Head}& \text{Food}& \text{Education}& \text{Clothing}& \text{House}& \text{Others}& \text{Savings}\\ & & & & \text{rent}& & \\ \text{Expenditure (Rs.)}& 4000& 2500& 1000& 3500& 2500& 1500\end{array}$

Draw a bar graph to represent the data above.

Q. Find the values of p, q, r and s in the given cumulative frequency distribution.

$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 10& 3& p\\ 15& 10& q\\ 20& 25& r\\ 25& 7& s\\ 30& 5& 50\end{array}$

1. p = 0, q = 10, r = 35, s = 42
2. p = 3, q = 13, r = 28, s = 35
3. p = 3, q = 13, r = 35, s = 42
4. p = 3, q = 13, r = 38, s = 45

Q.

$$\begin{array}{cccccc}\text{Weekly wages (in ₹)}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{Number of workers}& 40& 39& 34& 30& 45\end{array}$$

What is the number of people whose wage is less than ₹400?

1. 40
2. 79
3. 139
4. 143

Q.

Find the median term of the following cumulative frequency distribution:
$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

1. 49.5

2. 54

3. 55

4. 53.5

Q.

What is the cumulative frequency of the modal class of the following distribution?

$\begin{array}{cccccccc}Class& 3-6& 6-9& 9-12& 12-15& 15-18& 18-2& 21-24\\ Frequency& 7& 13& 10& 23& 4& 21& 16\end{array}$

Q.

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

Q.

Relation R in set A = {1, 2, 3 . . . . 13, 14} is defined as R = {(x, y): 3x - y = 0}. Write the relation in roster form.

Q.

The following table gives the frequency distribution of marks obtained by $28$ students.

$\begin{array}{ccccc}\text{Marks}& 30& 31& 32& 33\\ \text{Frequency}& 5& 7& 10& 6\end{array}$

Construct the cumulative frequency table for the given data.

1. $5,14,22,30$

2. $5,12,22,28$

3. $7,12,22,28$

4. $5,12,20,28$

Q. Class {10 - 20, 20 - 30, 30 - 40 , 40 - 50}, f {5, 7, 8, 9}- Calculate the cumulative frequency.

1. 5
2. 20
3. 12
4. 29

Q. If the ${10}^{th}$ term of an A.P. is $52$ and the ${17}^{th}$ term is $20$ more than the ${13}^{th}$ term, find the A.P.

Q. Question 13(ii)
The following are the ages of 300 patients getting medical treatment in a hospital on a particular day
$\begin{array}{ccccccc}Age\left(inyear\right)& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ Numberofpatients& 60& 42& 55& 70& 53& 20\end{array}$
Form

(ii) More than type cumulative frequency distribution.

Q.

In a frequency distribution, ogives are graphical representation of

1. Frequency

2. Cumulative frequency

3. Relative frequency

4. Raw data