Practice worksheet for finding mean, median, mode, and range of number sets.

Of course! Let's solve each problem step by step, calculating the Mean, Median, Mode, and Range for each set of numbers.

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🔢 Definitions:

- Mean = Sum of all numbers ÷ Count of numbers
- Median = Middle number when data is ordered (if even count, average of two middle numbers)
- Mode = Number(s) that appear most frequently
- Range = Largest number – Smallest number

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## 🟢 Problem 1: `3, 0, 0, 2, 0, 3, 0, 2, 2, 2, 3`

Step 1: Order the data
→ `0, 0, 0, 0, 2, 2, 2, 2, 3, 3, 3`

Step 2: Mean
Sum = 0+0+0+0+2+2+2+2+3+3+3 = 17
Count = 11
Mean = 17 ÷ 11 ≈ 1.55

Step 3: Median
Middle value (6th in 11 numbers) → 2

Step 4: Mode
0 appears 4 times → most frequent → 0

Step 5: Range
Max = 3, Min = 0 → 3 - 0 = 3

✔ Answer 1:
- Mean: 1.55
- Median: 2
- Mode: 0
- Range: 3

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## 🟢 Problem 2: `40, 61, 95, 79, 9, 50, 80, 63, 109, 42`

Step 1: Order the data
→ `9, 40, 42, 50, 61, 63, 79, 80, 95, 109`

Step 2: Mean
Sum = 9+40+42+50+61+63+79+80+95+109 = 528
Count = 10
Mean = 528 ÷ 10 = 52.8

Step 3: Median
Even count → average of 5th and 6th: (61 + 63) ÷ 2 = 62

Step 4: Mode
All numbers appear once → No mode (or “none”)

Step 5: Range
Max = 109, Min = 9 → 109 - 9 = 100

✔ Answer 2:
- Mean: 52.8
- Median: 62
- Mode: None
- Range: 100

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## 🟢 Problem 3: `90, 50, 70, 80, 70, 60, 20, 30, 80, 90, 20`

Step 1: Order the data
→ `20, 20, 30, 50, 60, 70, 70, 80, 80, 90, 90`

Step 2: Mean
Sum = 20+20+30+50+60+70+70+80+80+90+90 = 660
Count = 11
Mean = 660 ÷ 11 = 60

Step 3: Median
Middle value (6th) → 70

Step 4: Mode
20, 70, 80, 90 each appear twice → Multiple modes: 20, 70, 80, 90

Step 5: Range
Max = 90, Min = 20 → 90 - 20 = 70

✔ Answer 3:
- Mean: 60
- Median: 70
- Mode: 20, 70, 80, 90
- Range: 70

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## 🟢 Problem 4: `98, 100, 65, 78, 98, 35, 100, 45, 50`

Step 1: Order the data
→ `35, 45, 50, 65, 78, 98, 98, 100, 100`

Step 2: Mean
Sum = 35+45+50+65+78+98+98+100+100 = 569
Count = 9
Mean = 569 ÷ 9 ≈ 63.22

Step 3: Median
Middle value (5th) → 78

Step 4: Mode
98 and 100 each appear twice → 98, 100

Step 5: Range
Max = 100, Min = 35 → 100 - 35 = 65

✔ Answer 4:
- Mean: 63.22
- Median: 78
- Mode: 98, 100
- Range: 65

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## 🟢 Problem 5: `8, 2, 9, 4, 2, 7, 8, 0, 4, 1`

Step 1: Order the data
→ `0, 1, 2, 2, 4, 4, 7, 8, 8, 9`

Step 2: Mean
Sum = 0+1+2+2+4+4+7+8+8+9 = 45
Count = 10
Mean = 45 ÷ 10 = 4.5

Step 3: Median
Even count → average of 5th and 6th: (4 + 4) ÷ 2 = 4

Step 4: Mode
2, 4, and 8 each appear twice → 2, 4, 8

Step 5: Range
Max = 9, Min = 0 → 9 - 0 = 9

✔ Answer 5:
- Mean: 4.5
- Median: 4
- Mode: 2, 4, 8
- Range: 9

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## 🟢 Problem 6: `32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20`

Step 1: Order the data
Let’s sort:

→ `6, 8, 10, 10, 11, 12, 12, 15, 16, 16, 17, 18, 18, 20, 21, 21, 23, 24, 24, 24, 29, 30, 31, 32, 32, 32, 35, 36, 39, 40`

Total numbers = 30

Step 2: Mean
Sum = Let’s add them up carefully:

Grouped for ease:
- 6, 8 → 14
- 10×2 → 20
- 11 → 11
- 12×2 → 24
- 15 → 15
- 16×2 → 32
- 17 → 17
- 18×2 → 36
- 20 → 20
- 21×2 → 42
- 23 → 23
- 24×3 → 72
- 29 → 29
- 30 → 30
- 31 → 31
- 32×3 → 96
- 35 → 35
- 36 → 36
- 39 → 39
- 40 → 40

Now add:

14 + 20 = 34
+11 = 45
+24 = 69
+15 = 84
+32 = 116
+17 = 133
+36 = 169
+20 = 189
+42 = 231
+23 = 254
+72 = 326
+29 = 355
+30 = 385
+31 = 416
+96 = 512
+35 = 547
+36 = 583
+39 = 622
+40 = 662

Sum = 662
Count = 30
Mean = 662 ÷ 30 ≈ 22.07

Step 3: Median
Even count → average of 15th and 16th values:

From sorted list:
Position 15: 21
Position 16: 21
Median = (21 + 21) ÷ 2 = 21

Step 4: Mode
Count frequencies:
- 24 appears 3 times
- 32 appears 3 times
- Others appear ≤2 times

→ 24 and 32 are both modes (bimodal)

Step 5: Range
Max = 40, Min = 6 → 40 - 6 = 34

✔ Answer 6:
- Mean: 22.07
- Median: 21
- Mode: 24, 32
- Range: 34

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## ✔ Final Answers Summary:

| Problem | Mean | Median | Mode | Range |
|---------|----------|--------|------------------|-------|
| 1 | 1.55 | 2 | 0 | 3 |
| 2 | 52.8 | 62 | None | 100 |
| 3 | 60 | 70 | 20, 70, 80, 90 | 70 |
| 4 | 63.22 | 78 | 98, 100 | 65 |
| 5 | 4.5 | 4 | 2, 4, 8 | 9 |
| 6 | 22.07 | 21 | 24, 32 | 34 |

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