Math worksheet for calculating mean and median of number sets.

Let’s solve each problem step by step. For each set of numbers, we’ll find:

- Mean: Add all the numbers together, then divide by how many numbers there are.
- Median: Put the numbers in order from smallest to largest. If there’s an odd number of values, the median is the middle one. If even, it’s the average of the two middle numbers.

We’ll go one by one.

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Problem 1: 22, 2, 5, 12, 9

Step 1: Order them → 2, 5, 9, 12, 22
→ Median = middle number = 9

Step 2: Mean = (2 + 5 + 9 + 12 + 22) ÷ 5 = 50 ÷ 5 = 10

✔ Mean: 10, Median: 9

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Problem 2: 4, 10, 12, 12, 15, 17, 23, 28

Step 1: Already ordered? Let’s check: yes, sorted.

There are 8 numbers → even → median = average of 4th and 5th numbers.

4th = 12, 5th = 15 → (12 + 15) ÷ 2 = 27 ÷ 2 = 13.5

Step 2: Sum = 4+10+12+12+15+17+23+28 = let’s add:

4+10=14; +12=26; +12=38; +15=53; +17=70; +23=93; +28=121

Mean = 121 ÷ 8 = 15.125

✔ Mean: 15.125, Median: 13.5

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Problem 3: 19, 19, 27, 36, 64

Ordered? Yes.

Odd count → median = middle = 3rd number = 27

Sum = 19+19+27+36+64 = 19+19=38; +27=65; +36=101; +64=165

Mean = 165 ÷ 5 = 33

✔ Mean: 33, Median: 27

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Problem 4: 53, 44, 10, 45, 59, 97, 77

First, order them: 10, 44, 45, 53, 59, 77, 97

7 numbers → median = 4th = 53

Sum = 10+44=54; +45=99; +53=152; +59=211; +77=288; +97=385

Mean = 385 ÷ 7 = 55

✔ Mean: 55, Median: 53

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Problem 5: 8, 8, 12, 14, 8, 2, 1

Order: 1, 2, 8, 8, 8, 12, 14

7 numbers → median = 4th = 8

Sum = 1+2+8+8+8+12+14 = 1+2=3; +8=11; +8=19; +8=27; +12=39; +14=53

Mean = 53 ÷ 7 ≈ 7.571 (we can leave as fraction or decimal — usually decimal is fine)

But let’s keep exact: 53/7 = 7.571... but for worksheet, maybe round to 2 decimals? Or leave as is? Since others are whole or .5, perhaps write as 7.57 or just 53/7? But looking at other problems, they expect decimal.

Actually, let’s calculate exactly: 53 ÷ 7 = 7.571428... → we’ll use 7.57 if rounding, but better to be precise. Wait — let me check sum again:

Numbers: 8,8,12,14,8,2,1 → that’s three 8s → 8×3=24; plus 12+14=26; plus 2+1=3 → total 24+26=50+3=53 → correct.

So mean = 53/7 ≈ 7.57 (if rounded to hundredths). But since this is a math worksheet, sometimes they want exact fractions. However, looking at problem 2, we had 15.125, so decimals are okay.

I’ll write 7.57 (rounded), but actually, let’s see — maybe keep as mixed number? No, probably decimal is expected.

Wait — let’s do exact division: 53 ÷ 7 = 7 and 4/7 ≈ 7.571 → I think for consistency, we’ll use two decimal places unless it terminates.

But problem 2 was 15.125 — which is exact. So perhaps we should give exact value.

Actually, 53/7 is approximately 7.571, but let’s write it as 7.57 for simplicity? Or better — let’s check if any instruction says. None, so I’ll use exact decimal where possible, else round reasonably.

Alternatively, maybe the worksheet expects simplified answers. Let’s proceed with exact calculation.

For now, I’ll write 7.57 (but note: it’s repeating). Actually, no — let’s recalculate sum to be sure.

List: 1,2,8,8,8,12,14 → 1+2=3; 8+8+8=24; 12+14=26; total 3+24=27+26=53 → yes.

53 ÷ 7 = 7.57142857... → perhaps write as 7.57 or 7.6? But to be accurate, let's keep more digits or use fraction? Since other problems have nice numbers, maybe I made a mistake?

No, it’s correct. I’ll write 7.57 (rounded to two decimals).

But let’s hold on — perhaps the teacher expects exact value. Looking back, problem 2 had 15.125 which is exact. So for this, 53/7 is not terminating, so maybe leave as fraction? But the blank says “Mean: ___” — likely decimal.

I think for school level, they might accept 7.57 or 7.6. But to be precise, let’s calculate all means as decimals with up to 3 places if needed.

Actually, let’s do this: for non-terminating, round to two decimal places.

So 53 ÷ 7 = 7.571... → 7.57

Median is 8.

✔ Mean: 7.57, Median: 8

But wait — let me double-check ordering: original: 8,8,12,14,8,2,1 → sorted: 1,2,8,8,8,12,14 → yes, 4th is 8.

Okay.

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Problem 6: 2, 5, 3, 4, 8, 2, 5, 3, 30, 31, 2

Count: 11 numbers.

First, sort them: 2,2,2,3,3,4,5,5,8,30,31

Median = 6th number (since 11 numbers, middle is 6th) → positions: 1:2, 2:2, 3:2, 4:3, 5:3, 6:4 → so median = 4

Sum: let’s add: 2+2+2=6; +3+3=12; +4=16; +5+5=26; +8=34; +30=64; +31=95

Total sum = 95

Mean = 95 ÷ 11 ≈ 8.636 → round to 8.64

✔ Mean: 8.64, Median: 4

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Problem 7: 17, 12, 15, 14, 12

Sort: 12,12,14,15,17

Median = 3rd = 14

Sum = 12+12+14+15+17 = 12+12=24; +14=38; +15=53; +17=70

Mean = 70 ÷ 5 = 14

✔ Mean: 14, Median: 14

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Problem 8: 31, 92, 25, 69, 80, 31, 29

Sort: 25,29,31,31,69,80,92

7 numbers → median = 4th = 31

Sum = 25+29=54; +31=85; +31=116; +69=185; +80=265; +92=357

Mean = 357 ÷ 7 = 51

✔ Mean: 51, Median: 31

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Problem 9: 48, 40, 53, 43, 52, 46

Sort: 40,43,46,48,52,53

6 numbers → even → median = average of 3rd and 4th: 46 and 48 → (46+48)/2 = 94/2 = 47

Sum = 40+43=83; +46=129; +48=177; +52=229; +53=282

Mean = 282 ÷ 6 = 47

✔ Mean: 47, Median: 47

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Problem 10: 36, 45, 52, 40, 38, 41, 50, 48

Sort: 36,38,40,41,45,48,50,52

8 numbers → median = average of 4th and 5th: 41 and 45 → (41+45)/2 = 86/2 = 43

Sum = 36+38=74; +40=114; +41=155; +45=200; +48=248; +50=298; +52=350

Mean = 350 ÷ 8 = 43.75

✔ Mean: 43.75, Median: 43

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Problem 11: 8, 9, 9, 8, 2, 3, 2, 3, 1

Sort: 1,2,2,3,3,8,8,9,9

9 numbers → median = 5th = 3

Sum = 1+2+2+3+3+8+8+9+9 = let’s group: 1; 2+2=4; 3+3=6; 8+8=16; 9+9=18 → total 1+4=5; +6=11; +16=27; +18=45

Mean = 45 ÷ 9 = 5

✔ Mean: 5, Median: 3

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Problem 12: 116, 130, 120, 125, 140, 125

Sort: 116,120,125,125,130,140

6 numbers → median = average of 3rd and 4th: both 125 → (125+125)/2 = 125

Sum = 116+120=236; +125=361; +125=486; +130=616; +140=756

Mean = 756 ÷ 6 = 126

✔ Mean: 126, Median: 125

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Problem 13: 18, 16, 20, 9, 7, 5, 12, 17

Sort: 5,7,9,12,16,17,18,20

8 numbers → median = average of 4th and 5th: 12 and 16 → (12+16)/2 = 28/2 = 14

Sum = 5+7=12; +9=21; +12=33; +16=49; +17=66; +18=84; +20=104

Mean = 104 ÷ 8 = 13

✔ Mean: 13, Median: 14

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Problem 14: 61, 21, 80, 46, 37, 70, 59, 65, 46, 39

Sort: 21,37,39,46,46,59,61,65,70,80

10 numbers → median = average of 5th and 6th: 46 and 59 → (46+59)/2 = 105/2 = 52.5

Sum = let’s add carefully:

21+37=58; +39=97; +46=143; +46=189; +59=248; +61=309; +65=374; +70=444; +80=524

Mean = 524 ÷ 10 = 52.4

✔ Mean: 52.4, Median: 52.5

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Now, compiling all answers:

1. Mean: 10, Median: 9
2. Mean: 15.125, Median: 13.5
3. Mean: 33, Median: 27
4. Mean: 55, Median: 53
5. Mean: 7.57 (or 53/7 ≈7.571), Median: 8
→ To be consistent, let's use 7.57 (but actually, 53÷7=7.571428..., so perhaps write 7.57)
However, in problem 2 we used 15.125, so for accuracy, maybe write 7.571? But that’s messy.
Alternatively, since it's a worksheet, perhaps they expect rounded to two decimals. I'll use 7.57.
But let me check: 53/7 = 7 4/7, which is approximately 7.57. Okay.

Actually, upon second thought, for problem 5, sum is 53, count 7, so mean is 53/7. In decimal, it's 7.571... but for school, often they round to nearest hundredth. So 7.57.

Similarly, problem 6: 95/11≈8.636→8.64

Problem 14: 52.4 and 52.5 — exact.

So I'll stick with that.

Final Answers:

1. Mean: 10, Median: 9
2. Mean: 15.125, Median: 13.5
3. Mean: 33, Median: 27
4. Mean: 55, Median: 53
5. Mean: 7.57, Median: 8
6. Mean: 8.64, Median: 4
7. Mean: 14, Median: 14
8. Mean: 51, Median: 31
9. Mean: 47, Median: 47
10. Mean: 43.75, Median: 43
11. Mean: 5, Median: 3
12. Mean: 126, Median: 125
13. Mean: 13, Median: 14
14. Mean: 52.4, Median: 52.5

Note: For problem 5 and 6, I rounded to two decimal places. If your teacher wants exact fractions, you can write 53/7 and 95/11, but since the worksheet has blanks like "___", decimals are likely expected.

Also, for problem 2, 15.125 is exact, so we kept it.

Now, writing final answer as per format.

Final Answer:
1. Mean: 10, Median: 9
2. Mean: 15.125, Median: 13.5
3. Mean: 33, Median: 27
4. Mean: 55, Median: 53
5. Mean: 7.57, Median: 8
6. Mean: 8.64, Median: 4
7. Mean: 14, Median: 14
8. Mean: 51, Median: 31
9. Mean: 47, Median: 47
10. Mean: 43.75, Median: 43
11. Mean: 5, Median: 3
12. Mean: 126, Median: 125
13. Mean: 13, Median: 14
14. Mean: 52.4, Median: 52.5