Finding Mode for Grouped Data When Class Intervals Are Given

Q.

Assertion-and-Reason Type

Each question consists of two statements, namely, Assertion (A) and Reason (R).For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ Considerthefollowingfrequency& Thevalueofthevariablewhich\\ distribution:& occursmostoftenisthemode\\ \begin{array}{ccccccc}Classinterval& 3-6& 6-9& 9-12& 12-15& 15-18& 18-21\\ Frequency& 2& 5& 21& 23& 10& 12\end{array}& \\ Themodeoftheabovedatais\mathrm{12.4.}& \end{array}$

The correct answer is:(a)/(b)/(c)/(d).

Q.

The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years): 5-15 15-25 25-35 35-45 45-55 55-65
No. of students: 6 11 21 23 14 5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Q.

Compute the mode from the following data:
$\begin{array}{ccccccccccc}\text{Class}& & & & & & & & & & \\ \text{interval}& 1-5& 6-10& 11-15& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45& 46-50\\ \text{Frequency}& 3& 8& 13& 18& 28& 20& 13& 8& 6& 4\end{array}$

Q. The mode of the following frequency distribution is

Class Interval	Frquency
0-10	4
10-20	6
20-30	8
30-40	10
40-50	7
50-60	5

1. 30
2. 35
3. 34
4. 37

Q.

The age wise participation of students in the Annual Function of a school is shown in the following distribution.
$\begin{array}{cccccccc}\text{Age (in years)}& 5-7& 7-9& 9-11& 11-13& 13-15& 15-17& 17-19\\ \text{Number of}& & & & & & & \\ \text{students}& x& 15& 18& 30& 50& 48& x\end{array}$

Find the missing frequencies when the sum of frequencies is $181$. Also, find the mode of the data.

Q.

Find the mode of the following frequency distribution:
$\begin{array}{cccccc}\text{Marks}& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 12& 35& 45& 25& 13\end{array}$

Q. The mode of the following frequency distribution is

Class Interval	Frquency
0-10	5
10-20	10
20-30	8
30-40	13
40-50	12

1. $\frac{115}{3}$
2. 40
3. $\frac{98}{3}$
4. 34

Q.

Heights of students of Class X are given in the foloowing frequency distribution:

Height (in cm)	150−155	155−160	160−165	165−170	170−175
Number of students	15	8	20	12	5

Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency. [CBSE 2014]

Q.

Compute the mode from the following data:
$\begin{array}{cccccccc}\text{Size}& 45-55& 55-65& 65-75& 75-85& 85-95& 95-105& 105-115\\ \text{Frequency}& 7& 12& 17& 30& 32& 6& 10\end{array}$

Q. Identify the modal class, the upper limit of the modal class and the lower limit of the modal class for the given data:
$\begin{array}{ccccccc}Age\left(inyears\right)& 5-15& 15-25& 25-35& 35-45& 45-55& 55-65\\ Numberofpatients& 6& 11& 21& 23& 14& 5\end{array}$

1. 15-25, 11, 21
2. 35-45, 45, 35
3. 35-45, 35, 45
4. 15-55, 11, 31

Q. The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:

Shirt Size:	37	38	39	40	41	42	43	44
Number of persons:	15	25	39	41	36	17	15	12

Find the modal shirt size worn by the group.

Q.

In the following data, find the values of $p$ and $q$ Also, find the median class and modal class.

$\begin{array}{ccc}\text{Class}& \text{Frequency(f)}& \text{Cumulative~frequency(cf)}\\ 100-200& 11& 11\\ 200-300& 12& p\\ 300-400& 10& 13\\ 400-500& q& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\end{array}$

Q.

The monthly income of 100 families are given as below:
$\begin{array}{cc}& \\ \text{Income in (in Rs)}& \text{Number of families}\\ 0-5000& 8\\ 5000-10000& 26\\ 10000-15000& 41\\ 15000-20000& 16\\ 20000-25000& 3\\ 25000-30000& 3\\ 30000-35000& 2\\ 35000-40000& 1\end{array}$
Calculate the modal income.

Q. For the following distribution:
Below: 10 20 30 40 50 60

Number of students: 3 12 27 57 75 80

the modal class is

(a) 10-20 (b) 20-30 (c) 30-40 (d) 50-60

Q.

Compute the mode from the following data:
$\begin{array}{cccccccc}\text{Age(in years)}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30& 30-35\\ \text{Number of patients}& 6& 11& 18& 24& 17& 13& 5\end{array}$

Q.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Lifetimes (in hours): 0-20 20-40 40-60 60-80 80-100 100-120
No. of components: 10 35 52 61 38 29
Determine the modal lifetimes of the components.

Q.

Find the mode of the following data:

Class	0−20	20−40	40−60	60−80
Frequency	15	6	18	10

Q.

Find the mode of the following distribution:
$\begin{array}{ccccccccc}\text{Class interval}& 10-14& 14-18& 18-22& 22-26& 26-30& 30-34& 34-38& 38-42\\ \text{Frequency}& 8& 6& 11& 20& 25& 22& 10& 4\end{array}$

Q. Write down the decimal expansions of the rational numbers which have terminating decimal expansions.
(i) $\frac{13}{3125}$ (ii) $\frac{17}{8}$ (iii) $\frac{15}{1600}$ (iv) $\frac{23}{2^3{5}^2}$ (v) $\frac{6}{15}$ (vi) $\frac{35}{50}$

Q.

Given below is the distribution of total household expenditure of 200 manual workers in a city.
$\begin{array}{cc}\text{Expenditure (in Rs.)}& \text{No. of manual workers}\\ 1000-1500& 24\\ 1500-2000& 40\\ 2000-2500& 31\\ 2500-3000& 28\\ 3000-3500& 32\\ 3500-4000& 23\\ 4000-4500& 17\\ 4500-5000& 5\end{array}$
Find the expenditure done by maximum number of manual workers.

Q.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

Number of cars	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 − 60	60 − 70	70 − 80
Frequency	7	14	13	12	20	11	15	8

Q.

Compute the mode of the following data: [CBSE 2013]

Class	0−20	20−40	40−60	60−80	80−100
Frequency	25	16	28	20	5

Q.

The following is the distribution of height of students of a certain class in a certain city:
Height (in cms): 160-162 163-165 166-168 169-171 172-174
No. of students: 15 118 142 127 18
Find the average height of maximum number of students.

Q.

Consider the following table:

$\begin{array}{cccccc}Classinterval& 10-14& 14-18& 18-22& 22-26& 26-30\\ Frequency& 5& 11& 16& 25& 19\end{array}$

The mode of the above data is

(a) 23.5 (b) 24 (c) 24.4 (d) 25

Q.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
$\begin{array}{cccc}\text{Runs scored}& \text{Number of bastsman}& \text{Runs scored}& \text{Number of bastsman}\\ 3000-4000& 4& 7000-8000& 6\\ 4000-5000& 18& 8000-9000& 3\\ 5000-6000& 9& 9000-10000& 1\\ 6000-7000& 7& 10000-11000& 1\end{array}$
Find the mode of the data.

Q.

Question 26

Encircle the odd one of the following:

(a) (-3, 3)
(b) (-5, 5)
(c) (-6, 1)
(d) (-8, 8)

Q. Find the mode of the following frequency distribution: [CBSE 2014]

Marks	10−20	20−30	30−40	40−50	50−60
Frequency	12	35	45	25	13

Q. The table below shows the salaries of 280 persons :
$\begin{array}{cc}\text{Salary(In thousand Rs.)}& \text{No. of Persons}\\ 5-10& 49\\ 10-15& 133\\ 15-20& 63\\ 20-25& 15\\ 25-30& 6\\ 30-35& 7\\ 35-40& 4\\ 40-45& 2\\ 45-50& 1\end{array}$
Calculate the median salary of the data.

Q.

The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency: 3 5 16 12 13 20 5 4 1 1

Q. Find the mode of the given data: [CBSE 2015]

Class interval	0−20	20−40	40−60	60−80
Frequency	15	6	18	10