# Statistics - Mode and Range

**Question 1**

The

**mo**de is the

**mo**st common number. Find the mode for the following data sets:

a) $3,4,5,5,6,7$

a
$5$

Question ID: 70010010010

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The most frequent number is $5$ in the list. The mode is the most common number, therefore the mode is $5$.

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b) $5,6,8,9,9,10,11,12,12,12,15$

a
$12$

Question ID: 70010010020

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The most frequent number is $12$ in the list. The mode is the most common number, therefore the mode is $12$.

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c) $7,2,9,3,5,2,6$

a
$2$

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The most frequent number is $2$ in the list. The mode is the most common number, therefore the mode is $2$.

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d) $17,14,19,15,14,16,18,14,19,8$

a
$14$

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The most frequent number is $14$ in the list. The mode is the most common number, therefore the mode is $14$.

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e) $0.2,0.5,0.2,0.3,0.7,0.9$

a
$0.2$

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The most frequent number is $0.2$ in the list. It doesn't matter that it is a decimal. The mode is the most common number, therefore the mode is $0.2$.

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f) $82,15,45,88,43,32,15,67,42,19$

a
$15$

Question ID: 70010010060

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The most frequent number is $15$ in the list. The mode is the most common number, therefore the mode is $15$.

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g) $6,2,8,3,5,9,1,4,7$

a
There is no mode

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s
If there is no result that occurs more frequently than others, there is no mode.

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h) $153,122,122,153,122,160,118$

a
$122$

Question ID: 70010010080

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The most frequent number is $122$ in the list. The mode is the most common number, therefore the mode is $122$.

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i) $1.86,2.47,5.22,0.8,9.4,0.2,8.2,0.8,1.45,9.33,1.45,2.22,16.8,2.13,0.8$

a
$0.8$

Question ID: 70010010090

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The most frequent number is $0.8$ in the list. It doesn't matter that it is a decimal. The mode is the most common number, therefore the mode is $0.8$.

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j) $2,6,3,2,8,3,5,4,9,11$

a
$2$ and $3$

Question ID: 70010010100

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The mode is the most common number. Here $2$ and $3$ both occur twice, making them both the most common number. It is fine to have multiple modes. Therefore the mode is both $2$ and $3$.

Question ID: 70010010100

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k) Red, Green, Blue, Green, Orange, Yellow, Black, Blue, Purple, Blue

a
Blue

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The most frequent colour is blue in the list. It doesn't matter if it is a word or a number. The mode is the most common result, therefore the mode is blue.

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l) $512,632,912,723,321,723,123,428,539,632,582,675,531,723$

a
$723$

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m) Hat, Coat, Scarf, Shirt, Coat, Coat, Scarf, Shirt, Hat, Shirt, Hat, Coat, Watch

a
Coat

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n) Three, Twenty, Sixteen, Eight, Sixteen, Eight, Nine, Eight, Nine, Fifteen, Twelve, Eight, Sixteen, Eighteen, Four, Sixteen, Eleven

a
Sixteen and Eight

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o) $0.001,0.001,0.01,0.1,1.0,0.1,0.001,1.0,10.01$

a
$0.001$

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**Question 2**

Find the mode for the following data set:

a)

Result |
Frequency |

Red |
4 |

Blue |
5 |

Green |
3 |

a
Blue

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Find the result that has the highest frequence, meaning it occurs most often. The mode is the most common, in this table, blue has the highest frequence, therefore blue is the mode.

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b)

Result |
Frequency |

20 |
5 |

21 |
11 |

22 |
17 |

23 |
11 |

24 |
4 |

a
$22$

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Find the result that has the highest frequence, meaning it occurs most often. The mode is the most common, in this table, the number $22$ has the highest frequence, therefore $22$ is the mode.

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c)

Score |
Frequency |

94 |
2 |

95 |
0 |

96 |
5 |

97 |
2 |

98 |
5 |

99 |
5 |

100 |
6 |

a
$100$

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d)

Length |
Frequency |

5m |
7 |

6m |
3 |

7m |
8 |

8m |
4 |

9m |
7 |

10m |
1 |

a
$7$m

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**Question 3**

The range is the difference between the largest result and the smallest result. Find the range for the following data sets:

a) $10,15$

a
$5$

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Largest result: $15$

Smallest result: $10$

Largest-Smallest$=15-10=5$

So $5$ is the range.

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b) $72,32$

a
$40$

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Largest result: $72$

Smallest result: $32$

Largest-Smallest$=72-32=40$

So $40$ is the range.

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c) $3,5,9$

a
$6$

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Largest result: $9$

Smallest result: $3$

Largest-Smallest$=9-3=6$

So $6$ is the range.

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d) $0.4,0.6,0.7,0.7,0.9$

a
$0.5$

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Largest result: $0.9$

Smallest result: $0.4$

Largest-Smallest$=0.9-0.4=0.5$

So $0.5$ is the range.

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e) $8,4,1,8,14,3,19,4,3$

a
$16$

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f) $53,12,83,28,84,29$

a
$72$

Question ID: 70010030060

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g) $835,632,563,642,146,864,346,887,24,567,382$

a
$863$

Question ID: 70010030070

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h) $6.3,9.2,4.7,0.3,6.2,7.3,8.5,5.9,3.6,0.2,1.2$

a
$9$

Question ID: 70010030080

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i) $8392.35,1235,524,5327,7432,2363,7432,345,742,2364,9202$

a
$8857$

Question ID: 70010030090

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**Question 4**

Find the range for the following data set:

a)

Result |
Frequency |

42 |
8 |

43 |
20 |

44 |
6 |

a
$2$

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Largest result: $44$

Smallest result: $42$

The frequency has no effect on the mode.

Largest-Smallest$=44-42=2$

So $2$ is the range.

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b)

Score |
Frequency |

10 |
9 |

11 |
11 |

12 |
4 |

13 |
22 |

14 |
18 |

15 |
3 |

a
$19$

Question ID: 70010040020

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Largest result: $22$

Smallest result: $3$

The frequency has no effect on the mode.

Largest-Smallest$=22-4=19$

So $19$ is the range.

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**Question 5**

Find the mode and range for the following data set:

a) $7,4,2,19,2$

a
Mode$=2$

Range$=17$

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b) $53,61,27,72,27,33,63$

a
Mode$=27$

Range$=45$

Question ID: 70010050020

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c) $0.4,1.8,0.5,2.6,9.3,10.4,0.5,1.4,1.8,18$

a
Mode$=0.5$ and $1.8$

Range$=17.6$

Question ID: 70010050030

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d) $724,901,235,666,253,842,702,503,125,812$

a
There is no mode

Range$=776$

Question ID: 70010050040

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**Question 6**

For the following data find both the mode and range.

a)

a
Mode$=9$

Range$=8$

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b)

72 |
28 |
92 |
13 |

20 |
55 |
14 |
20 |

94 |
6 |
17 |
39 |

a
Mode$=20$

Range$=88$

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c)

0.5 |
2.6 |
9.4 |
2.5 |

9.2 |
4.5 |
1 |
16 |

9.9 |
4.4 |
8.4 |
9.1 |

20 |
1.6 |
3.3 |
1.9 |

a
There is no mode.

Range$=19.5$

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d)

724 |
925 |
101 |
205 |
925 |

670 |
836 |
877 |
162 |
599 |

281 |
281 |
678 |
445 |
544 |

925 |
777 |
836 |
532 |
532 |

207 |
924 |
670 |
836 |
909 |

a
Mode$=925$ and $836$

Range$=824$

Question ID: 70010060040

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**Question 1**

The

**mo**de is the

**mo**st common number. Find the mode for the following data sets:

a) $3,4,5,5,6,7$

b) $5,6,8,9,9,10,11,12,12,12,15$

c) $7,2,9,3,5,2,6$

d) $17,14,19,15,14,16,18,14,19,8$

e) $0.2,0.5,0.2,0.3,0.7,0.9$

f) $82,15,45,88,43,32,15,67,42,19$

g) $6,2,8,3,5,9,1,4,7$

h) $153,122,122,153,122,160,118$

i) $1.86,2.47,5.22,0.8,9.4,0.2,8.2,0.8,1.45,9.33,1.45,2.22,16.8,2.13,0.8$

j) $2,6,3,2,8,3,5,4,9,11$

k) Red, Green, Blue, Green, Orange, Yellow, Black, Blue, Purple, Blue

l) $512,632,912,723,321,723,123,428,539,632,582,675,531,723$

m) Hat, Coat, Scarf, Shirt, Coat, Coat, Scarf, Shirt, Hat, Shirt, Hat, Coat, Watch

n) Three, Twenty, Sixteen, Eight, Sixteen, Eight, Nine, Eight, Nine, Fifteen, Twelve, Eight, Sixteen, Eighteen, Four, Sixteen, Eleven

o) $0.001,0.001,0.01,0.1,1.0,0.1,0.001,1.0,10.01$

**Question 2**

Find the mode for the following data set:

a)

Result |
Frequency |

Red |
4 |

Blue |
5 |

Green |
3 |

b)

Result |
Frequency |

20 |
5 |

21 |
11 |

22 |
17 |

23 |
11 |

24 |
4 |

c)

Score |
Frequency |

94 |
2 |

95 |
0 |

96 |
5 |

97 |
2 |

98 |
5 |

99 |
5 |

100 |
6 |

d)

Length |
Frequency |

5m |
7 |

6m |
3 |

7m |
8 |

8m |
4 |

9m |
7 |

10m |
1 |

**Question 3**

The range is the difference between the largest result and the smallest result. Find the range for the following data sets:

a) $10,15$

b) $72,32$

c) $3,5,9$

d) $0.4,0.6,0.7,0.7,0.9$

e) $8,4,1,8,14,3,19,4,3$

f) $53,12,83,28,84,29$

g) $835,632,563,642,146,864,346,887,24,567,382$

h) $6.3,9.2,4.7,0.3,6.2,7.3,8.5,5.9,3.6,0.2,1.2$

i) $8392.35,1235,524,5327,7432,2363,7432,345,742,2364,9202$

**Question 4**

Find the range for the following data set:

a)

Result |
Frequency |

42 |
8 |

43 |
20 |

44 |
6 |

b)

Score |
Frequency |

10 |
9 |

11 |
11 |

12 |
4 |

13 |
22 |

14 |
18 |

15 |
3 |

**Question 5**

Find the mode and range for the following data set:

a) $7,4,2,19,2$

b) $53,61,27,72,27,33,63$

c) $0.4,1.8,0.5,2.6,9.3,10.4,0.5,1.4,1.8,18$

d) $724,901,235,666,253,842,702,503,125,812$

**Question 6**

For the following data find both the mode and range.

b)

72 |
28 |
92 |
13 |

20 |
55 |
14 |
20 |

94 |
6 |
17 |
39 |

c)

0.5 |
2.6 |
9.4 |
2.5 |

9.2 |
4.5 |
1 |
16 |

9.9 |
4.4 |
8.4 |
9.1 |

20 |
1.6 |
3.3 |
1.9 |

d)

724 |
925 |
101 |
205 |
925 |

670 |
836 |
877 |
162 |
599 |

281 |
281 |
678 |
445 |
544 |

925 |
777 |
836 |
532 |
532 |

207 |
924 |
670 |
836 |
909 |

__Answers__

**Question 1**

a) $5$

b) $12$

c) $2$

d) $14$

e) $0.2$

f) $15$

g) There is no mode

h) $122$

i) $0.8$

j) $2$ and $3$

k) Blue

l) $723$

m) Coat

n) Sixteen and Eight

o) $0.001$

**Question 2**

a) Blue

b) $22$

c) $100$

d) $7$m

**Question 3**

a) $5$

b) $40$

c) $6$

d) $0.5$

e) $16$

f) $72$

g) $863$

h) $9$

i) $8857$

**Question 4**

a) $2$

b) $19$

**Question 5**

a) Mode$=2$

Range$=17$

b) Mode$=27$

Range$=45$

c) Mode$=0.5$ and $1.8$

Range$=17.6$

d) There is no mode

Range$=776$

**Question 6**

a) Mode$=9$

Range$=8$

b) Mode$=20$

Range$=88$

c) There is no mode.

Range$=19.5$

d) Mode$=925$ and $836$

Range$=824$

**Question 1**

The

**mo**de is the

**mo**st common number. Find the mode for the following data sets:

a) $3,4,5,5,6,7$

b) $5,6,8,9,9,10,11,12,12,12,15$

c) $7,2,9,3,5,2,6$

d) $17,14,19,15,14,16,18,14,19,8$

e) $0.2,0.5,0.2,0.3,0.7,0.9$

f) $82,15,45,88,43,32,15,67,42,19$

g) $6,2,8,3,5,9,1,4,7$

h) $153,122,122,153,122,160,118$

i) $1.86,2.47,5.22,0.8,9.4,0.2,8.2,0.8,1.45,9.33,1.45,2.22,16.8,2.13,0.8$

j) $2,6,3,2,8,3,5,4,9,11$

k) Red, Green, Blue, Green, Orange, Yellow, Black, Blue, Purple, Blue

l) $512,632,912,723,321,723,123,428,539,632,582,675,531,723$

m) Hat, Coat, Scarf, Shirt, Coat, Coat, Scarf, Shirt, Hat, Shirt, Hat, Coat, Watch

n) Three, Twenty, Sixteen, Eight, Sixteen, Eight, Nine, Eight, Nine, Fifteen, Twelve, Eight, Sixteen, Eighteen, Four, Sixteen, Eleven

o) $0.001,0.001,0.01,0.1,1.0,0.1,0.001,1.0,10.01$

**Question 2**

Find the mode for the following data set:

a)

Result |
Frequency |

Red |
4 |

Blue |
5 |

Green |
3 |

b)

Result |
Frequency |

20 |
5 |

21 |
11 |

22 |
17 |

23 |
11 |

24 |
4 |

c)

Score |
Frequency |

94 |
2 |

95 |
0 |

96 |
5 |

97 |
2 |

98 |
5 |

99 |
5 |

100 |
6 |

d)

Length |
Frequency |

5m |
7 |

6m |
3 |

7m |
8 |

8m |
4 |

9m |
7 |

10m |
1 |

**Question 3**

The range is the difference between the largest result and the smallest result. Find the range for the following data sets:

a) $10,15$

b) $72,32$

c) $3,5,9$

d) $0.4,0.6,0.7,0.7,0.9$

e) $8,4,1,8,14,3,19,4,3$

f) $53,12,83,28,84,29$

g) $835,632,563,642,146,864,346,887,24,567,382$

h) $6.3,9.2,4.7,0.3,6.2,7.3,8.5,5.9,3.6,0.2,1.2$

i) $8392.35,1235,524,5327,7432,2363,7432,345,742,2364,9202$

**Question 4**

Find the range for the following data set:

a)

Result |
Frequency |

42 |
8 |

43 |
20 |

44 |
6 |

b)

Score |
Frequency |

10 |
9 |

11 |
11 |

12 |
4 |

13 |
22 |

14 |
18 |

15 |
3 |

**Question 5**

Find the mode and range for the following data set:

a) $7,4,2,19,2$

b) $53,61,27,72,27,33,63$

c) $0.4,1.8,0.5,2.6,9.3,10.4,0.5,1.4,1.8,18$

d) $724,901,235,666,253,842,702,503,125,812$

**Question 6**

For the following data find both the mode and range.

b)

72 |
28 |
92 |
13 |

20 |
55 |
14 |
20 |

94 |
6 |
17 |
39 |

c)

0.5 |
2.6 |
9.4 |
2.5 |

9.2 |
4.5 |
1 |
16 |

9.9 |
4.4 |
8.4 |
9.1 |

20 |
1.6 |
3.3 |
1.9 |

d)

724 |
925 |
101 |
205 |
925 |

670 |
836 |
877 |
162 |
599 |

281 |
281 |
678 |
445 |
544 |

925 |
777 |
836 |
532 |
532 |

207 |
924 |
670 |
836 |
909 |

__Answers__

**Question 1**

a) $5$

b) $12$

c) $2$

d) $14$

e) $0.2$

f) $15$

g) There is no mode

h) $122$

i) $0.8$

j) $2$ and $3$

k) Blue

l) $723$

m) Coat

n) Sixteen and Eight

o) $0.001$

**Question 2**

a) Blue

b) $22$

c) $100$

d) $7$m

**Question 3**

a) $5$

b) $40$

c) $6$

d) $0.5$

e) $16$

f) $72$

g) $863$

h) $9$

i) $8857$

**Question 4**

a) $2$

b) $19$

**Question 5**

a) Mode$=2$

Range$=17$

b) Mode$=27$

Range$=45$

c) Mode$=0.5$ and $1.8$

Range$=17.6$

d) There is no mode

Range$=776$

**Question 6**

a) Mode$=9$

Range$=8$

b) Mode$=20$

Range$=88$

c) There is no mode.

Range$=19.5$

d) Mode$=925$ and $836$

Range$=824$

__Solutions__

**Question 1**

a) The most frequent number is $5$ in the list. The mode is the most common number, therefore the mode is $5$.

b) The most frequent number is $12$ in the list. The mode is the most common number, therefore the mode is $12$.

c) The most frequent number is $2$ in the list. The mode is the most common number, therefore the mode is $2$.

d) The most frequent number is $14$ in the list. The mode is the most common number, therefore the mode is $14$.

e) The most frequent number is $0.2$ in the list. It doesn't matter that it is a decimal. The mode is the most common number, therefore the mode is $0.2$.

f) The most frequent number is $15$ in the list. The mode is the most common number, therefore the mode is $15$.

g) If there is no result that occurs more frequently than others, there is no mode.

h) The most frequent number is $122$ in the list. The mode is the most common number, therefore the mode is $122$.

i) The most frequent number is $0.8$ in the list. It doesn't matter that it is a decimal. The mode is the most common number, therefore the mode is $0.8$.

j) The mode is the most common number. Here $2$ and $3$ both occur twice, making them both the most common number. It is fine to have multiple modes. Therefore the mode is both $2$ and $3$.

k) The most frequent colour is blue in the list. It doesn't matter if it is a word or a number. The mode is the most common result, therefore the mode is blue.

l)

m)

n)

o)

**Question 2**

a) Find the result that has the highest frequence, meaning it occurs most often. The mode is the most common, in this table, blue has the highest frequence, therefore blue is the mode.

b) Find the result that has the highest frequence, meaning it occurs most often. The mode is the most common, in this table, the number $22$ has the highest frequence, therefore $22$ is the mode.

c)

d)

**Question 3**

a) Largest result: $15$

Smallest result: $10$

Largest-Smallest$=15-10=5$

So $5$ is the range.

b) Largest result: $72$

Smallest result: $32$

Largest-Smallest$=72-32=40$

So $40$ is the range.

c) Largest result: $9$

Smallest result: $3$

Largest-Smallest$=9-3=6$

So $6$ is the range.

d) Largest result: $0.9$

Smallest result: $0.4$

Largest-Smallest$=0.9-0.4=0.5$

So $0.5$ is the range.

e)

f)

g)

h)

i)

**Question 4**

a) Largest result: $44$

Smallest result: $42$

The frequency has no effect on the mode.

Largest-Smallest$=44-42=2$

So $2$ is the range.

b) Largest result: $22$

Smallest result: $3$

The frequency has no effect on the mode.

Largest-Smallest$=22-4=19$

So $19$ is the range.

**Question 5**

a)

b)

c)

d)

**Question 6**

a)

b)

c)

d)