Calculate Mode using Grouping Method from the following grouped data

X	Frequency
10	3
20	5
30	3
40	1
50	2
60	5
70	13
80	9
90	2

Solution:
Mode using Grouping Method :
1) In column-I, write the original frequency
2) In column-II, combine the frequency two by two, starting from top
3) In column-III, combine the frequency two by two, starting from second
4) In column-IV, combine the frequency three by three, starting from top
5) In column-V, combine the frequency three by three, starting from second
6) In column-VI, combine the frequency three by three, starting from third

Grouping Table :

x	I Frequency	II (1+2)	III (2+3)	IV (1+2+3)	V (2+3+4)	VI (3+4+5)
10	3
		3+5=8
20	5			3+5+3=11
			5+3=8
30	3				5+3+1=9
		3+1=4
40	1					3+1+2=6
			1+2=3
50	2			1+2+5=8
		2+5=7
60	5				2+5+13=20
			5+13=18
70	13					5+13+9=27
		13+9=22
80	9			13+9+2=24
			9+2=11
90	2

1) 13 is the maximum value in the column-I and it is an individual frequency of x 70. Therefore, we have tick(✓) this x.
2) 22 is the maximum value in the column-II and it is the sum of 13 and 9; i.e., of x 70 and 80. Therefore, we have tick(✓) this both x.
3) 18 is the maximum value in the column-III and it is the sum of 5 and 13; i.e., of x 60 and 70. Therefore, we have tick(✓) this both x.
4) 24 is the maximum value in the column-IV and it is the sum of 13, 9, and 2; i.e, of x 70, 80 and 90. Therefore, we have tick(✓) this three x.
5) 20 is the maximum value in the column-V and it is the sum of 2, 5, and 13; i.e, of x 50, 60 and 70. Therefore, we have tick(✓) this three x.
6) 27 is the maximum value in the column-VI and it is the sum of 5, 13, and 9; i.e, of x 60, 70 and 80. Therefore, we have tick(✓) this three x.

Analysis Table :

Column	I	II	III	IV	V	VI	Total
Max Frequency	13	22	18	24	20	27
10							-
20							-
30							-
40							-
50					✓		1
60			✓		✓	✓	3
70	✓	✓	✓	✓	✓	✓	6
80		✓		✓		✓	3
90				✓			1

Since 70 has the maximum ticks 6. So mode is 70.

---