Math worksheet for practicing mean, median, mode, and range calculations with various number sets.

Let’s solve each problem step by step. We’ll find the mean, median, mode, and range for each set of numbers.

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Problem 1: {2, 5, 3, 4, 8, 2, 5, 3, 10, 11, 2}

Step 1: Order the numbers
→ 2, 2, 2, 3, 3, 4, 5, 5, 8, 10, 11

Step 2: Mean (average)
Add all numbers:
2+2+2+3+3+4+5+5+8+10+11 = let’s add:
2+2=4; +2=6; +3=9; +3=12; +4=16; +5=21; +5=26; +8=34; +10=44; +11=55
Total = 55
Count = 11 numbers
Mean = 55 ÷ 11 = 5

Step 3: Median (middle number)
Ordered list has 11 numbers → middle is the 6th number
Positions: 1(2), 2(2), 3(2), 4(3), 5(3), 6(4), 7(5), 8(5), 9(8), 10(10), 11(11)
Median = 4

Step 4: Mode (most frequent)
2 appears 3 times → most frequent
Mode = 2

Step 5: Range (max - min)
Max = 11, Min = 2 → Range = 11 - 2 = 9

✔ Problem 1:
Order: 2, 2, 2, 3, 3, 4, 5, 5, 8, 10, 11
Mean: 5
Median: 4
Mode: 2
Range: 9

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Problem 2: {53, 38, 43, 47, 38, 45, 53, 41, 38}

Step 1: Order
→ 38, 38, 38, 41, 43, 45, 47, 53, 53

Step 2: Mean
Sum: 38+38+38+41+43+45+47+53+53
Group: (38×3)=114; 41+43=84; 45+47=92; 53+53=106
Total = 114+84=198; +92=290; +106=396
Count = 9
Mean = 396 ÷ 9 = 44

Step 3: Median
9 numbers → 5th is middle
Positions: 1(38), 2(38), 3(38), 4(41), 5(43), 6(45), 7(47), 8(53), 9(53)
Median = 43

Step 4: Mode
38 appears 3 times → most frequent
Mode = 38

Step 5: Range
Max = 53, Min = 38 → 53 - 38 = 15

✔ Problem 2:
Order: 38, 38, 38, 41, 43, 45, 47, 53, 53
Mean: 44
Median: 43
Mode: 38
Range: 15

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Problem 3: {0.2, 0.8, 0.4, 0.3, 0.4, 1.3, 0.2, 0.4}

Step 1: Order
→ 0.2, 0.2, 0.3, 0.4, 0.4, 0.4, 0.8, 1.3

Step 2: Mean
Sum: 0.2+0.2=0.4; +0.3=0.7; +0.4=1.1; +0.4=1.5; +0.4=1.9; +0.8=2.7; +1.3=4.0
Total = 4.0
Count = 8
Mean = 4.0 ÷ 8 = 0.5

Step 3: Median
8 numbers → average of 4th and 5th
4th = 0.4, 5th = 0.4 → (0.4 + 0.4)/2 = 0.4

Step 4: Mode
0.4 appears 3 times → most frequent
Mode = 0.4

Step 5: Range
Max = 1.3, Min = 0.2 → 1.3 - 0.2 = 1.1

✔ Problem 3:
Order: 0.2, 0.2, 0.3, 0.4, 0.4, 0.4, 0.8, 1.3
Mean: 0.5
Median: 0.4
Mode: 0.4
Range: 1.1

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Problem 4: {-8, 4, 2, -5, 4, -1, -3, 4, -5, 1, 7}

Step 1: Order
→ -8, -5, -5, -3, -1, 1, 2, 4, 4, 4, 7

Step 2: Mean
Sum: Let’s group negatives and positives
Negatives: -8 + (-5) + (-5) + (-3) + (-1) = -22
Positives: 1 + 2 + 4 + 4 + 4 + 7 = 22
Total = -22 + 22 = 0
Count = 11
Mean = 0 ÷ 11 = 0

Step 3: Median
11 numbers → 6th is middle
Positions: 1(-8), 2(-5), 3(-5), 4(-3), 5(-1), 6(1), 7(2), 8(4), 9(4), 10(4), 11(7)
Median = 1

Step 4: Mode
4 appears 3 times → most frequent
Mode = 4

Step 5: Range
Max = 7, Min = -8 → 7 - (-8) = 7 + 8 = 15

✔ Problem 4:
Order: -8, -5, -5, -3, -1, 1, 2, 4, 4, 4, 7
Mean: 0
Median: 1
Mode: 4
Range: 15

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Problem 5: {81, 75, 73, 79, 75, 89, 72, 80}

Step 1: Order
→ 72, 73, 75, 75, 79, 80, 81, 89

Step 2: Mean
Sum: 72+73=145; +75=220; +75=295; +79=374; +80=454; +81=535; +89=624
Total = 624
Count = 8
Mean = 624 ÷ 8 = 78

Step 3: Median
8 numbers → average of 4th and 5th
4th = 75, 5th = 79 → (75 + 79)/2 = 154/2 = 77

Step 4: Mode
75 appears twice → only one that repeats
Mode = 75

Step 5: Range
Max = 89, Min = 72 → 89 - 72 = 17

✔ Problem 5:
Order: 72, 73, 75, 75, 79, 80, 81, 89
Mean: 78
Median: 77
Mode: 75
Range: 17

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Problem 6: {1.3, 2.9, 1.8, 1.4, 2.0, 2.2, 1.8, 2.6}

Step 1: Order
→ 1.3, 1.4, 1.8, 1.8, 2.0, 2.2, 2.6, 2.9

Step 2: Mean
Sum: 1.3+1.4=2.7; +1.8=4.5; +1.8=6.3; +2.0=8.3; +2.2=10.5; +2.6=13.1; +2.9=16.0
Total = 16.0
Count = 8
Mean = 16.0 ÷ 8 = 2.0

Step 3: Median
8 numbers → average of 4th and 5th
4th = 1.8, 5th = 2.0 → (1.8 + 2.0)/2 = 3.8/2 = 1.9

Step 4: Mode
1.8 appears twice → only repeat
Mode = 1.8

Step 5: Range
Max = 2.9, Min = 1.3 → 2.9 - 1.3 = 1.6

✔ Problem 6:
Order: 1.3, 1.4, 1.8, 1.8, 2.0, 2.2, 2.6, 2.9
Mean: 2.0
Median: 1.9
Mode: 1.8
Range: 1.6

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Problem 7: {4.3, 3.8, 3.3, 4.0, 3.8, 4.3, 4.2, 4.3}

Step 1: Order
→ 3.3, 3.8, 3.8, 4.0, 4.2, 4.3, 4.3, 4.3

Step 2: Mean
Sum: 3.3+3.8=7.1; +3.8=10.9; +4.0=14.9; +4.2=19.1; +4.3=23.4; +4.3=27.7; +4.3=32.0
Total = 32.0
Count = 8
Mean = 32.0 ÷ 8 = 4.0

Step 3: Median
8 numbers → average of 4th and 5th
4th = 4.0, 5th = 4.2 → (4.0 + 4.2)/2 = 8.2/2 = 4.1

Step 4: Mode
4.3 appears 3 times → most frequent
Mode = 4.3

Step 5: Range
Max = 4.3, Min = 3.3 → 4.3 - 3.3 = 1.0

✔ Problem 7:
Order: 3.3, 3.8, 3.8, 4.0, 4.2, 4.3, 4.3, 4.3
Mean: 4.0
Median: 4.1
Mode: 4.3
Range: 1.0

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Problem 8: {6, -9, 1, 6, 0, -5, -1, 6, -5, 2, 10}

Step 1: Order
→ -9, -5, -5, -1, 0, 1, 2, 6, 6, 6, 10

Step 2: Mean
Sum: Negatives: -9 + (-5) + (-5) + (-1) = -20
Positives: 0 + 1 + 2 + 6 + 6 + 6 + 10 = 31
Total = -20 + 31 = 11
Count = 11
Mean = 11 ÷ 11 = 1

Step 3: Median
11 numbers → 6th is middle
Positions: 1(-9), 2(-5), 3(-5), 4(-1), 5(0), 6(1), 7(2), 8(6), 9(6), 10(6), 11(10)
Median = 1

Step 4: Mode
6 appears 3 times → most frequent
Mode = 6

Step 5: Range
Max = 10, Min = -9 → 10 - (-9) = 10 + 9 = 19

✔ Problem 8:
Order: -9, -5, -5, -1, 0, 1, 2, 6, 6, 6, 10
Mean: 1
Median: 1
Mode: 6
Range: 19

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Final Answer:

Problem 1:
Order: 2, 2, 2, 3, 3, 4, 5, 5, 8, 10, 11
Mean: 5
Median: 4
Mode: 2
Range: 9

Problem 2:
Order: 38, 38, 38, 41, 43, 45, 47, 53, 53
Mean: 44
Median: 43
Mode: 38
Range: 15

Problem 3:
Order: 0.2, 0.2, 0.3, 0.4, 0.4, 0.4, 0.8, 1.3
Mean: 0.5
Median: 0.4
Mode: 0.4
Range: 1.1

Problem 4:
Order: -8, -5, -5, -3, -1, 1, 2, 4, 4, 4, 7
Mean: 0
Median: 1
Mode: 4
Range: 15

Problem 5:
Order: 72, 73, 75, 75, 79, 80, 81, 89
Mean: 78
Median: 77
Mode: 75
Range: 17

Problem 6:
Order: 1.3, 1.4, 1.8, 1.8, 2.0, 2.2, 2.6, 2.9
Mean: 2.0
Median: 1.9
Mode: 1.8
Range: 1.6

Problem 7:
Order: 3.3, 3.8, 3.8, 4.0, 4.2, 4.3, 4.3, 4.3
Mean: 4.0
Median: 4.1
Mode: 4.3
Range: 1.0

Problem 8:
Order: -9, -5, -5, -1, 0, 1, 2, 6, 6, 6, 10
Mean: 1
Median: 1
Mode: 6
Range: 19