1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
12)
11)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
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
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
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)
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
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
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
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
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
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
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
23)
range = 10
mean = 4
median = 2
mode = 1
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
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
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
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)