Mode of Grouped Data

IMPORTANT

Mode of Grouped Data: Overview

In this topic, you will learn about the computation of mode of a discrete frequency distribution and frequency distribution with class interval.

Important Questions on Mode of Grouped Data

MEDIUM
IMPORTANT

The marks obtained by a set of students in an exam are recorded in a grouped frequency table. The maximum number of students are found to be in the range of 70-80 marks.

If the number of students in the ranges before and after the 70-80 range are equal, which of the following is the mode of the data?

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 0-50 50-100 100-150 150-200 200-250
Number of people a-10 a-5 a a+5 a+10

Where, 

a, is the median for the grouped data given below.

x 10 20 30 40 50
f 18 20 8 10 18

 

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 30-60 60-90 90-120 120-150 150-180
Number of people a÷5 a÷2 a 2a 5a

Where, 

a, is the median for the grouped data given below.

x 20 30 40 50 60
f 8 10 18 20 28

 

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 15-30 30-45 45-60 60-75 75-90
Number of people b=a-5 b-2 2 a+10 b-4

Where, 

a, is the median for the grouped data given below.

x 13 15 17 19 21
f 52 48 32 28 9

 

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 15-20 20-25 25-30 30-35 35-40
Number of people 2a 45 a a-5 4a

Where,

a, is the mean for the ungrouped data given below.

13.25, 10.25, 13.30, 14.20, 15.20, 16.30, 17.35, 20.15

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 10-20 20-30 30-40 40-50 50-60
Number of people a-2 a+8 50 2a-2 10

Where,

a, is the mean for the ungrouped data given below.

10.2, 12.5, 11.3, 14.5, 15.3, 16.6, 7.8, 9.8, 10.6, 11.4

HARD
IMPORTANT

Find the mode for the continuous data given below.

Class 10-15 15-20 20-25 25-30 30-35
Number of people a÷3 10 a a-5 5

Where,

a, is the mean for the ungrouped data given below.

15, 5, 20, 10, 20, 30, 5, 10, 15, 20

MEDIUM
IMPORTANT

In the following question given below, on solving the given statement, we get quantities I and II, solve both quantities and choose the correct option.

Quantity I: Find the mode value of the data given below:

2, 3, 5, 5, 6, 6, 7, 7, 7, 8, 9, 10, 10, 11, 11, 12

Quantity II: Find the mode value for the ungrouped data given below:

For the following data:

16, x-2, 18, x-2, x-2, x, 18, x+1, 23, 25, 24, 27, 26

If the median of the ungrouped data is 21, and 18<x<23.

MEDIUM
IMPORTANT

Find the mode for the given grouped frequency distribution.

Table I:

x 1 3 5 7 9
f b=a+0.67 38 b-10 2b-10 b+10

Where, 

a, is the mean for the grouped frequency distribution given below.

Table II:

x 5 10 15 20 25
f 6 12 18 24 30

 

MEDIUM
IMPORTANT

Find the mode for the given grouped frequency distribution.

Table I:

x 5 7 8 10 13
f 5 10 a 15 b

Where, 

a, is the mean for the grouped frequency distribution shown in table II, and the value of b is 50% more than the value of a.

Table II:

x 5 15 25 35 45
f 10 20 30 40 50

 

MEDIUM
IMPORTANT

Find the mode for the given grouped frequency distribution.

Table I:

x 10 20 30 40 50
f 9 18 a 36 a+18

Where, 

a, is the mean for the grouped frequency distribution given below.

Table II:

x 15 20 25 30 35
f 30 40 50 60 70

 

EASY
IMPORTANT

The mode of the data 12, 1, 10, 1, 9, 3, 4, 9, 7, 9 is:

EASY
IMPORTANT

Data about the times, in seconds, taken to run 100 metres by n adults are given in the following table.

Time xs 13.6x<15.4 15.4x<17.4 17.4x<19.8
No. adults f a b 27

By first investigating the possible values of a and of b, find the largest possible value of n, given that the modal class contains the slowest runners.

EASY
IMPORTANT

Four classes of continuous data are recorded as 1-7, 8-16, 17-20 and 21-25. The class 1-7 has a frequency of 84 and there is no modal class. Find the total frequency of the other three classes.

EASY
IMPORTANT

The histogram shows the lengths of 26 black rats.

Question Image

The modal class is

EASY
IMPORTANT

Height in cms:60-62 63-6566-6869-7172-74
No. of students: 1511814212718

Modal group is

HARD
IMPORTANT

Find the mode of the following data :

Marks No. of students
40-50 4
50-60 7
60-70 4
70-80 9
80-90 4

 

HARD
IMPORTANT

Find the mode of the following data :

MARKS No. of students
11-19 6
20-30 7
31-39 8
40-50 6

 

HARD
IMPORTANT

Find the mode of the following data :

Weight No. of students
51-59 4
60-70 7
71-79 5
80-90 9
91-99 4

 

HARD
IMPORTANT

Find the mode of the following data :

Family size No. of families
1-3 7
3-5 8
5-7 2
7-9 2
9-11 1
11-13 5