Mean Median Mode Range Worksheets - Math Monks - Free Printable

Explanation:
Let’s solve each problem one by one. For each set of numbers, we need to find:

- Mean: Add all numbers and divide by how many there are.
- Median: Put the numbers in order (smallest to largest), then find the middle number. If there’s an even number of values, average the two middle ones.
- Mode: The number that appears most often. There can be more than one mode, or none if all appear equally.
- Range: Largest number minus smallest number.

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Problem 1: 62, 10, 24, 24, 10, 62, 24, 10, 62, 62
First, count: 10 numbers.

Sort them: 10, 10, 10, 24, 24, 24, 62, 62, 62, 62
→ Mean: Sum = 10+10+10+24+24+24+62+62+62+62
= (10×3) + (24×3) + (62×4) = 30 + 72 + 248 = 350
Mean = 350 ÷ 10 = 35

→ Median: Even count → average of 5th and 6th numbers.
Sorted: positions 1–10 → 5th = 24, 6th = 24 → median = (24+24)/2 = 24

→ Mode: Which appears most?
10 appears 3 times, 24 appears 3 times, 62 appears 4 times → 62 is mode.

→ Range: max = 62, min = 10 → 62 − 10 = 52

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Problem 2: 3, 17, 17, 11, 8, 13, 5, 18
Count: 8 numbers.

Sort: 3, 5, 8, 11, 13, 17, 17, 18
→ Mean: Sum = 3+5+8+11+13+17+17+18 =
3+5=8; 8+8=16; 16+11=27; 27+13=40; 40+17=57; 57+17=74; 74+18=92
Mean = 92 ÷ 8 = 11.5

→ Median: 8 numbers → average of 4th and 5th: 11 and 13 → (11+13)/2 = 12

→ Mode: 17 appears twice; others once → 17

→ Range: 18 − 3 = 15

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Problem 3: 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13
Count: 15 numbers.

Sort: 5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48
→ Mean: Let’s add carefully:
5 + 6 + 6 = 17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50
50 + 13 = 63
63 + 13 = 76
76 + 15 = 91
91 + 18 = 109
109 + 24 = 133
133 + 28 = 161
161 + 33 = 194
194 + 36 = 230
230 + 48 = 278
Mean = 278 ÷ 15 = 18.533... → 18.53 (but usually round to 2 decimals or keep as fraction). Since it's a worksheet, likely expect decimal: 278/15 = 18.53 (or 18.5 if rounding to 1 decimal). Let’s double-check sum:

Alternative grouping:
(5 + 48) = 53
(6 + 36) = 42
(6 + 33) = 39
(9 + 28) = 37
(11 + 24) = 35
(13 + 18) = 31
(13 + 15) = 28
+ extra 13 (middle) = 13
Now add: 53+42=95; +39=134; +37=171; +35=206; +31=237; +28=265; +13=278 ✔

So mean = 278/15 = 18.53 (or 18.5 if allowed). But many worksheets accept exact fraction or decimal — let’s use 18.53 (2 decimals).

→ Median: 15 numbers → 8th number (since (15+1)/2 = 8th). Sorted list:
1:5, 2:6, 3:6, 4:9, 5:11, 6:13, 7:13, 8:13, 9:15, … → median = 13

→ Mode: 13 appears 3 times; 6 appears 2 times; others once → 13

→ Range: 48 − 5 = 43

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Problem 4: 8, 9, 5, 8, 3, 7, 3, 9, 2
Count: 9 numbers.

Sort: 2, 3, 3, 5, 8, 8, 9, 9, 9
→ Mean: Sum = 2+3+3+5+8+8+9+9+9
= 2+3+3=8; +5=13; +8=21; +8=29; +9=38; +9=47; +9=56
Mean = 56 ÷ 9 ≈ 6.22 (56/9 = 6.222…)

→ Median: 9 numbers → 5th number = 8

→ Mode: 9 appears 3 times; 3 and 8 appear 2 times → 9

→ Range: 9 − 2 = 7

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Problem 5: 6, 3, 9, 5, 7, 2, 5, 5, 3
Count: 9 numbers.

Sort: 2, 3, 3, 5, 5, 5, 6, 7, 9
→ Mean: Sum = 2+3+3+5+5+5+6+7+9
= 2+3+3=8; +5=13; +5=18; +5=23; +6=29; +7=36; +9=45
Mean = 45 ÷ 9 = 5

→ Median: 5th number = 5

→ Mode: 5 appears 3 times; 3 appears 2 times → 5

→ Range: 9 − 2 = 7

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Problem 6: 86, 13, 60, 55, 61, 97, 30, 98, 79, 52, 18
Count: 11 numbers.

Sort: 13, 18, 30, 52, 55, 60, 61, 79, 86, 97, 98
→ Mean: Sum =
13 + 18 = 31
31 + 30 = 61
61 + 52 = 113
113 + 55 = 168
168 + 60 = 228
228 + 61 = 289
289 + 79 = 368
368 + 86 = 454
454 + 97 = 551
551 + 98 = 649
Mean = 649 ÷ 11 = 59 exactly? 11 × 59 = 649 → yes! So 59

→ Median: 11 numbers → 6th number = 60

→ Mode: All numbers appear once → no repeated value → no mode
But sometimes worksheets say “none” or leave blank. Since the box expects a value, and many accept “none”, but let’s check: any repeats? 13,18,30,52,55,60,61,79,86,97,98 — all unique → mode = none

→ Range: 98 − 13 = 85

Now compile all answers clearly:

1. Mean: 35, Median: 24, Mode: 62, Range: 52
2. Mean: 11.5, Median: 12, Mode: 17, Range: 15
3. Mean: 18.53 (or 278/15), Median: 13, Mode: 13, Range: 43
4. Mean: 6.22, Median: 8, Mode: 9, Range: 7
5. Mean: 5, Median: 5, Mode: 5, Range: 7
6. Mean: 59, Median: 60, Mode: none, Range: 85

But since this is a worksheet with blank boxes, likely expects decimals rounded reasonably, and “none” for mode if no repeat.

However, in many school worksheets, they may expect mode as “none” or leave blank — but the box is there, so safest to write “none”.

Let me verify problem 3 mean again: 278 ÷ 15 = 18.533… → often written as 18.53 or 18.5. Since other means like 11.5 are one decimal, maybe use one decimal: 18.5.

Check problem 4: 56/9 = 6.222… → 6.2 if one decimal.

But looking at problem 2: 92/8 = 11.5 → they used .5, so one decimal is fine.

So adjust:
- P1: 35.0 → but integer, just 35
- P2: 11.5
- P3: 18.5
- P4: 6.2
- P5: 5.0 → just 5
- P6: 59

Yes, that’s consistent.

Final verified answers:

1. Mean: 35, Median: 24, Mode: 62, Range: 52
2. Mean: 11.5, Median: 12, Mode: 17, Range: 15
3. Mean: 18.5, Median: 13, Mode: 13, Range: 43
4. Mean: 6.2, Median: 8, Mode: 9, Range: 7
5. Mean: 5, Median: 5, Mode: 5, Range: 7
6. Mean: 59, Median: 60, Mode: none, Range: 85

Final Answer:
1. Mean: 35, Median: 24, Mode: 62, Range: 52
2. Mean: 11.5, Median: 12, Mode: 17, Range: 15
3. Mean: 18.5, Median: 13, Mode: 13, Range: 43
4. Mean: 6.2, Median: 8, Mode: 9, Range: 7
5. Mean: 5, Median: 5, Mode: 5, Range: 7
6. Mean: 59, Median: 60, Mode: none, Range: 85