Frequency

Q. Explain the difference between a frequency distribution and a cumulative frequency distribution.

Q. The Cumulative Frequency of a class-interval is the sum of frequencies of that class and the classes which ________________ it.

1. Neither succeed nor precede
2. Succeed or precede
3. Succeed (come after)
4. Precede (come before)

Q.

Concentration of SO2 (in ppm)	Number of days (frequency )
0.00 − 0.04	4
0.04 − 0.08	9
0.08 − 0.12	9
0.12 − 0.16	2
0.16 − 0.20	4
0.20 − 0.24	2
Total	30

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Q.

The value of π up to50 decimal places is given below:

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.

(ii) What are the most and the least frequently occurring digits?

Q.

What Is the Maximum Number of Instances That Can Be Created for an Abstract Class?

Q.

Three coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:

Outcome	$3$ heads	$2$ heads	$1$ head	No head
Frequency	$23$	$72$	$77$	$28$

If the three coins are simultaneously tossed again, compute the probability of $2$ heads coming up.

Q. In a competitive exam 50 students passed in English. 60 students passed in Mathematics. 40 students passed in both the subjects. None of them fail in both the subjects. Find the number of students who passed at least in one of the subjects ?

Q. The marks scored by 55 students in a test are given below:

Marks:	0-5	5-10	10-15	15-20	20-25	25-30	30-35
No. of students	2	6	13	17	11	4	2

Prepare a cumulative frequency table.

Q. Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

x:	10	30	50	70	90
f:	17	f1	32	f2	19

Total 120.

Q. Find the missing frequency (p) for the following distribution whose mean is 7.68.

x:	3	5	7	9	11	13
f:	6	8	15	p	8	4

Q. The number of times a particular item occurs in a given data is called its

(a) variation

(b) frequency

(c) cumulative frequency

(d) class-size

Q. Question 2
The range of the data 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11 and 20 is:

A) 10
B) 15
C) 18
D) 26

Q. Marks of students of a Class are represented in the frequency polygon shown below.

How many students got marks less than 20?

1. 39

Q. The birth rate per thousand in five countries over a period of time is show below:
$\begin{array}{cccccc}\text{Country}& \text{China}& \text{India}& \text{Germany}& \text{UK}& \text{Sweden}\\ \text{Birth rate per thousand}& 42& 35& 14& 28& 21\end{array}$

Represent the above data by a bar graph.

Q. Find the probability of of getting (I)9 (ii)7 and (iii)6 on throwing two dice.

Q. Prepare a continuous grouped frequency distribution from the following data.

$\begin{array}{cc}\text{Mid-Point}& \text{Frequency}\\ 5& 4\\ 15& 8\\ 25& 13\\ 35& 12\\ 45& 6\end{array}$

Also, find the size of class intervals.

Q. The graph below shows the number of people of different age groups staying in a hotel. Find the correct statement(s) among the options.

1. Total number of people in 0-20 age group is 10
2. Total number of people in 0-20 age group is 5
3. Maximum number of people are from age group of 21-30 years
4. Total number of people staying in the hotel is 35

Q. On a page of a telephone directory, there are 200 telephone numbers. The frequency distribution of the digits at their units place is given below:

Unit digit	0	1	2	3	4	5	6	7	8	9
Frequency	22	26	22	22	20	10	14	28	16	20

Without looking at the page, a number is chosen at random from the page. What is the probability that the digit at the unit's place of the number chosen is greater than 6?

Q.

Question 1 (i)
A survey conducted by an organization for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %):
$\begin{array}{ccc}\text{S.No.}& \text{Causes}& \text{Female fatality rate}\left(\%\right)\\ 1.& \text{Reproductive health conditions}& 31.8\\ 2.& \text{Neuropsychiatric conditions}& 25.4\\ 3.& \text{Injuries}& 12.4\\ 4.& \text{Cardiovascular conditions}& 4.3\\ 5.& \text{Respiratory conditions}& 4.1\\ 6.& \text{Other causes}& 22.0\end{array}$
(i) Represent the information given above graphically.

Q.

Find out how many times did 4 or a greater than 4 number appeared.

$$\begin{array}{ccccccc}Dice& 1& 2& 3& 4& 5& 6\\ Frequency& 10& 12& 6& 4& 8& 10\end{array}$$

1. 22

2. 20

3. 18

4. 15

Q. Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Ages (in years)	10−20	20−30	30−40	40−50	50−60	60−70
Number of patients	90	50	60	80	50	30

Construct the cumulative frequency table for the above data.

Q.

Question 4 (ii)
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
$\begin{array}{cc}\text{Length (in mm)}& \text{Number of leaves}\\ 118-126& 3\\ 127-135& 5\\ 136-144& 9\\ 145-153& 12\\ 154-162& 5\\ 163-171& 4\\ 172-180& 2\end{array}$
(ii) Is there any other suitable graphical representation for the same data?

Q. The following information is regarding marks in English, obtained out of 80.
How many students obtained marks less than 40?

1. 2
2. 5
3. 17
4. 7

Q.

Three coins were tossed $30$ times simultaneously. Each time the number of heads occurring was noted down as follows: $012212313013112201213001123220$Prepare a frequency distribution table for the data given above.

Q.

Question 3 (iii)
The relative humidity (in %) of a certain city for a month of 30 days was as follows:
$$\begin{array}{cccccccccc}98.1& 98.6& 99.2& 90.3& 86.5& 95.3& 92.9& 96.3& 94.2& 95.1\\ 89.2& 92.3& 97.1& 93.5& 92.7& 95.1& 97.2& 93.3& 95.2& 97.3\\ 96.2& 92.1& 84.9& 90.2& 95.7& 98.3& 97.3& 96.1& 92.1& 89\end{array}$$
(iii) What is the range of this data?

Q.

How do I find class midpoints $?$

Q.

Find out how many times did 4 or a greater than 4 number appeared.

$$\begin{array}{ccccccc}Dice& 1& 2& 3& 4& 5& 6\\ Frequency& 10& 12& 6& 4& 8& 10\end{array}$$

1. 10

2. 12

3. 22

4. 13

Q.

In a college, the GPA of a student in different semesters is as follows:

7.5, 8.5, fail, 5.6, 6.6, fail, 9.0, fail. Find the frequency of him failing.

1. 3

2. 2

3. 1

4. 4

Q.

Question 4
Prepare a continuous grouped frequency distribution from the following data.

$\begin{array}{cc}\text{Mid-Point}& \text{Frequency}\\ 5& 4\\ 15& 8\\ 25& 13\\ 35& 12\\ 45& 6\end{array}$

Also, find the size of class intervals.

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. 1

3. 3

4. 1