## Note on Mode and Range

• Note
• Things to remember
• Exercise
• Quiz

#### Mode

The value which appears most often is called mode. If there is no repeated numbers then there is no mode. The mode f the of data is denoted by Mo.

Examples

• In the data, 4, 5, 6, 6, 6,7, 8. The mode is 6.
• In the data, 5, 6, 7, 8, 9, 10,11. There is no mode.
• In the data 5, 8, 8, 15, 18, 18. There are two modes 8 and 18.

#### Range

The range is the difference between the smallest and highest values in a set.To find the range, subtract the smallest values in the data set for the largest.

Examples

1. Five boys have weights 45 kg, 55 kg, 50kg, 60 kg and 65 kg. What is the range of their heights?
Solution:
Arranging the data in order,
45 kg, 50 kg, 55 kg, 60 kg and 65 kg
Largest value = 65 kg
Smallest value = 45 kg
Range = largest value - smallest value
= 65 kg - 45 kg
= 20 kg

2. What is the range of this group of numbers: 70, 20, 77, 50, 80, 60, 75, 40?
Solution:
Arranging the data in order,
20, 40, 50, 60, 70, 75, 77, 80
Largest value = 80
Smallest value = 20
Range = largest value - smallest value
= 80 - 20
= 20

• The mode is the number repeated most often.
• This list has two values that are repeated three times.
• The largest value is 13 and the smallest is 8, so the range is 13 - 8 = 5.
.

### Very Short Questions

Solution:

Given data

2, 3, 3, 2, 4, 5, 6, 3, 3, 5, 5, 4, 3, 2

By putting the list in order:

2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6

Here, 3 appears 5 times

So, (Mo) = 3

Solution:

Given data

3, 5, 6, 7, 8, 8, 8, 8, 9, 9

Here, 8 appears 4 times,

So, (Mo) = 8

Solution:

Given data

29cm, 34cm, 29cm, 26cm, 55cm, 34cm, 35cm, 40cm , 34cm, 56cm

By putting the list in order:

26cm, 29cm, 29cm, 34cm, 34cm, 34cm, 35cm , 40cm, 55cm, 56cm

Here 34 cm appears 3 times

So, Mode(Mo)=34 cm

Solution:

Given data

120, 125, 130, 125, 120, 135, 120, 140

By putting the list in order:

120, 120, 120, 125, 125, 130, 135, 140

Here 120 appears 3 times

So, Mode(Mo) =120

Solution:

Given data

99kg, 135kg, 182kg, 49kg, 189kg, 196kg, 78kg, 192kg, 182kg

By putting the list in order:

49kg, 78kg, 99kg, 135kg, 182kg, 182kg, 189kg, 192kg, 196kg

Here 182 kg appears 2 times

So, Mode(Mo) =182 kg

Solution:

Arranging the data in order:

38, 55, 59, 71, 75, 75, 75, 80

Largest value = 80, Smallest value = 38

Range = Largest value - Smallest value

=80 - 38

=42

Solution:

Arranging the data in order:

125 cm,128 cm, 130 cm, 139 cm, 140 cm, 141 cm

Largest value = 141 cm

Smallest value = 125 cm

Range =Largest value - Smallest value

= 141 cm - 125 cm

= 16 cm

Solution,

Arranging the data in order:

2, 7, 8, 9, 11, 12, 20, 20, 21, 22

Largest value = 22

Smallest value =2

so, Range = Largest value - Smallest value

= 22 - 2

=20

Solution,

Arranging the data in order:

110, 111, 112, 120, 130, 135, 140, 160

Largest value = 160

Smallest value =110

so, Range= Largest value - Smallest value

= 160 - 110

= 50

Solution:

Arranging the data in order:

8 cm, 10 cm, 11 cm, 12 cm, 14 cm, 15 cm, 19 cm, 20 cm

Largest value = 20 cm

Smallest value = 8 cm

so, Range = Largest value - Smallest value

= 20 cm - 8 cm

= 12 cm

Solution:

Given data

4.9 ft, 5.1 ft, 6.2 ft, 5.5 ft, 4.8 ft, 6.1 ft, 4.7 ft

Largest value=6.2 ft

Smallest value=4.7 ft

so, Range=L-S

=6.2 ft -4.7 ft

=1.5 ft

Solution:

Given

 Wages(Rs) 300 525 540 560 575 600 No of labour 20 25 8 15 27 29

here, Highest wage (H) = 600

Lowest wage (L) = 300

∴Range (R) = H-L

= Rs 600 - Rs 300

= Rs 300

Solution:

Highest marks scored by the student(H)=80

Lowest marks scored by the students(L)=40

$$\therefore$$ Range = H-L

=80-40

=40

Solution:

Arranging the data in order:

115, 116, 117, 120, 130, 135, 140, 150

Largest value (L)= 150

Smallest value (S) = 115

so, Range = L - S

= 150 - 115

= 35

Solution:

Largest value= 10

Smallest value=1

so, Range=Largest value - Smallest value

=10 - 1

=9

0%

7
4
5
3

125
135
120
115

30
55
35
45

7
9
11
8

35
30
48
45

20
25
22
18

35
45
30
40

10cm
17cm
12cm
15cm

12cm
15cm
10cm
17cm

2.7ft
3.2ft
1.7ft
1.5ft

85
90
105
95

188kg
182kg
175kg
185kg

45
30
35
40

7cm
5cm
8cm
6cm

6
3
2
4