1 of 13

1)

2)

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5)

6)

7)

8)

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24)

Averages and range (positive integers)

4 numbers:

mean = 10 range = 12

mode = 13

3 numbers:

mean = 3 mode = 2

3 numbers:

mean = 7 mode = 10

3 numbers:

mean = 8 median = 10 range = 8

3 numbers:

mean = 13 range = 8

find three sets

3 numbers:

mean = 6 median = 7 range = 11

3 numbers:

mode = 7 median = 7 mean = 6

4 numbers:

mean = 4 mode = 1

median = 2

4 numbers:

mean = 9 mode = 6

median = 7

4 numbers:

mean = 8 range = 8

median = 7

find three sets

4 numbers:

mean = 6 median = 6½

range = 11

4 numbers:

mean = 7½ mode = 6

median = 7

4 numbers:

mean = 4 range = 6

median = 3

find two sets

5 numbers: range = 5

mean = 6

median = 7

mode = 8

5 numbers: range = 5

mean = 4

median = 3

find three sets

5 numbers: range = 9

mean = 4

mode = 3

find two sets

5 numbers: range = 6

mean = 4

mode = 2

find two sets

5 numbers: range = 10

mean = 7

mode = 7

find three sets

range = 10

mean = 4

median = 2

mode = 1

  1. 4 numbers
  2. 5 numbers
  3. 6 numbers

5 numbers: range = 5

mean = 5

mode = 5

median = 5

find two sets

5 numbers: range = 10

mean = 10

mode = 10

median = 10

find three sets

6 numbers: range = 10

mean = 4

mode = 1

median = 2

5 numbers:

2, 5, n, 2n, 5n

mean = 2 × median – 1

find n

5 numbers: range = 10

mean = 4

mode = 1

median = 2

2 of 13

averages and spread

2 , 2 , 5

1 , 10 , 10

3 , 10 , 11

0 , 7 , 18

– 3 , – 1, 8 , 8

8 , 15 , 16 9 , 13 , 17 10 , 11 , 18

1 , 1 , 3 , 11

6 , 6 , 8 , 16

0 , 6 , 7 , 11

6 , 6 , 8 , 10

1 , 13 , 13 , 13

5 , 6 , 8 , 13 5 , 7 , 7, 13 5 5 9 13

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

3 of 13

12)

4 numbers:

range = 8

mean = 8

median = 7

find three sets

7 – b

7 + b

positive integers

a

total = 32

a + 8

5 7 7 13

2a + 22 = 32

a = 5

5 6 8 13

5 5 9 13

4 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

find three sets

7

7

positive integers

1

11

total = 35

total so far = 26

9

1 7 7 9 11

5 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

find three sets

7

7

positive integers

2

12

7

1 7 7 9 11

2 7 7 7 12

total = 35

total so far = 28

6 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

find three sets

7

7

positive integers

3

13

1 7 7 9 11

2 7 7 7 12

5

3 5 7 7 13

total = 35

total so far = 30

7 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

found three sets

7

7

positive integers

4

14

1 7 7 9 11

2 7 7 7 12

3 6 7 7 13

3

total = 35

total so far = 32

8 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

checked that there are three sets

7

7

positive integers

0

10

total = 35

total so far = 24

1 7 7 9 11

2 7 7 7 12

3 6 7 7 13

11

9 of 13

18)

5 numbers:

range = 10

mean = 7

mode = 7

alternative solution

7

7

positive integers

a

a + 10

b

total = 35

2a + b + 24 = 35

2a + b = 11

a = 0 , b = 11

a = 1 , b = 9

a = 2 , b = 7

1 7 7 9 11

2 7 7 7 11

a = 3 , b = 5

3 5 7 7 11

a = 4 , b = 3

b > a

b < a + 10

a = 5 , b = 1

b > a

10 of 13

23)

range = 10

mean = 4

median = 2

mode = 1

  1. 4 numbers
  2. 5 numbers
  3. 6 numbers

1

1

11

3

16

4

= 4

1

1

2

11

5

× 4

= 20

9

1

1

2 – n

7

11

2 + n

6

× 4

= 24

1

3

11 of 13

24)

median = n

mean = 2 × median – 1

= 2n – 1

2

5

n

5n

2n

8n + 7 = 5(2n – 1)

8n + 7 = 10n – 5

12 = 2n

6 = n

12 of 13

24)

mean = 2 × median – 1

= 2n – 1

n

? 6 6 6 36

3 4 6 12 ?

2 ? 6 18 ?

3 5 ? 39 65

2 ? ? 26 78

1 ? ? 13 ?

integers > 0

families

median = n

13 of 13

4 numbers with: mean = 8, mode = 7, range = 6

4 numbers with: mode = 8, mean = 7, range = 6

find a set of 5 consecutive integers with mean = 8

5 numbers with: mode = 4, median = 5, mean = 6, range = 7

5 numbers with: mode = n, median = n + 1, mean = n + 2, range = n + 3

find 2 (other) sets of numbers

(1)

(2)

(3)

(4)

find sets of integers

(5)