Math worksheet for calculating mean, median, mode, and range with six data sets.

Let's solve each problem step by step. For each data set, we'll:

1. Order the numbers from smallest to largest.
2. Find the Mean (average): sum of all numbers divided by count.
3. Find the Median: middle number when ordered (or average of two middle numbers if even count).
4. Find the Mode: most frequent number(s).
5. Find the Range: difference between highest and lowest values.

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1) Data: 61, 57, 49, 60, 45, 51, 57, 60, 53, 57, 55, 48, 65, 52

#### Step 1: Order
Arrange in ascending order:
45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65

#### Step 2: Mean
Sum = 45 + 48 + 49 + 51 + 52 + 53 + 55 + 57 + 57 + 57 + 60 + 60 + 61 + 65
= Let's add:
- 45+48=93
- 93+49=142
- 142+51=193
- 193+52=245
- 245+53=300
- 300+55=355
- 355+57=412
- 412+57=469
- 469+57=526
- 526+60=586
- 586+60=646
- 646+61=707
- 707+65=772

Total = 772
Count = 14
Mean = 772 ÷ 14 ≈ 55.14

#### Step 3: Median
14 numbers → median is average of 7th and 8th values:
- 7th = 55
- 8th = 57
- Median = (55 + 57)/2 = 56

#### Step 4: Mode
Most frequent: 57 appears 3 times (most frequent) → Mode = 57

#### Step 5: Range
Max = 65, Min = 45 → Range = 65 - 45 = 20

✔ Answer 1:
- Order: 45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65
- Mean: 55.14
- Median: 56
- Mode: 57
- Range: 20

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2) Data: 129, 113, 110, 123, 112, 115, 110, 124, 121, 113, 115, 121, 115

#### Step 1: Order
Sorted:
110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129

#### Step 2: Mean
Sum = 110+110=220
+112=332
+113=445
+113=558
+115=673
+115=788
+115=903
+121=1024
+121=1145
+123=1268
+124=1392
+129=1521

Sum = 1521
Count = 13
Mean = 1521 ÷ 13 ≈ 117

#### Step 3: Median
13 numbers → 7th value:
110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129
→ Median = 115

#### Step 4: Mode
115 appears 3 times → Mode = 115

#### Step 5: Range
Max = 129, Min = 110 → Range = 129 - 110 = 19

✔ Answer 2:
- Order: 110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129
- Mean: 117
- Median: 115
- Mode: 115
- Range: 19

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3) Data: 14, 7, 4, 8, 12, 4, 2, 9, 7, 11, 15, 12, 11, 8, 11, 7

#### Step 1: Order
Sorted:
2, 4, 4, 7, 7, 7, 8, 8, 9, 11, 11, 11, 12, 12, 14, 15

#### Step 2: Mean
Sum = 2+4=6
+4=10
+7=17
+7=24
+7=31
+8=39
+8=47
+9=56
+11=67
+11=78
+11=89
+12=101
+12=113
+14=127
+15=142

Sum = 142
Count = 16
Mean = 142 ÷ 16 = 8.875

#### Step 3: Median
16 numbers → average of 8th and 9th:
- 8th = 8
- 9th = 9
→ Median = (8+9)/2 = 8.5

#### Step 4: Mode
7 and 11 both appear 3 times → Bimodal: 7 and 11

#### Step 5: Range
Max = 15, Min = 2 → Range = 15 - 2 = 13

✔ Answer 3:
- Order: 2, 4, 4, 7, 7, 7, 8, 8, 9, 11, 11, 11, 12, 12, 14, 15
- Mean: 8.875
- Median: 8.5
- Mode: 7 and 11
- Range: 13

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4) Data: 83, 77, 81, 79, 85, 77, 76, 87, 81, 83, 77, 91, 81, 77

#### Step 1: Order
Sorted:
76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91

#### Step 2: Mean
Sum = 76 + 77×4 = 76 + 308 = 384
+79 = 463
+81×3 = 463 + 243 = 706
+83×2 = 706 + 166 = 872
+85 = 957
+87 = 1044
+91 = 1135

Sum = 1135
Count = 14
Mean = 1135 ÷ 14 ≈ 81.07

#### Step 3: Median
14 numbers → average of 7th and 8th:
- 7th = 81
- 8th = 81
→ Median = (81+81)/2 = 81

#### Step 4: Mode
77 appears 4 times → most frequent → Mode = 77

#### Step 5: Range
Max = 91, Min = 76 → Range = 91 - 76 = 15

✔ Answer 4:
- Order: 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91
- Mean: 81.07
- Median: 81
- Mode: 77
- Range: 15

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5) Data: 0.7, 0.2, 0.9, 1.2, 1.5, 0.4, 0.6, 0.2, 1.1, 0.3, 0.7, 0.2, 1.1

#### Step 1: Order
Sorted:
0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5

#### Step 2: Mean
Sum = 0.2×3 = 0.6
+0.3 = 0.9
+0.4 = 1.3
+0.6 = 1.9
+0.7 = 2.6
+0.7 = 3.3
+0.9 = 4.2
+1.1 = 5.3
+1.1 = 6.4
+1.2 = 7.6
+1.5 = 9.1

Sum = 9.1
Count = 13
Mean = 9.1 ÷ 13 ≈ 0.7

#### Step 3: Median
13 numbers → 7th value:
0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5
→ Median = 0.7

#### Step 4: Mode
0.2 appears 3 times → Mode = 0.2

#### Step 5: Range
Max = 1.5, Min = 0.2 → Range = 1.5 - 0.2 = 1.3

✔ Answer 5:
- Order: 0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5
- Mean: 0.7
- Median: 0.7
- Mode: 0.2
- Range: 1.3

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6) Data: 6.2, 5.6, 4.9, 5.1, 6.2, 5.7, 5.1, 4.7, 5.4, 6.2, 4.5, 6.4

#### Step 1: Order
Sorted:
4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4

#### Step 2: Mean
Sum = 4.5 + 4.7 = 9.2
+4.9 = 14.1
+5.1 = 19.2
+5.1 = 24.3
+5.4 = 29.7
+5.6 = 35.3
+5.7 = 41.0
+6.2 = 47.2
+6.2 = 53.4
+6.2 = 59.6
+6.4 = 66.0

Sum = 66.0
Count = 12
Mean = 66 ÷ 12 = 5.5

#### Step 3: Median
12 numbers → average of 6th and 7th:
- 6th = 5.4
- 7th = 5.6
→ Median = (5.4 + 5.6)/2 = 5.5

#### Step 4: Mode
6.2 appears 3 times → Mode = 6.2

#### Step 5: Range
Max = 6.4, Min = 4.5 → Range = 6.4 - 4.5 = 1.9

✔ Answer 6:
- Order: 4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4
- Mean: 5.5
- Median: 5.5
- Mode: 6.2
- Range: 1.9

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✔ Final Answers Summary:

| # | Order (sorted) | Mean | Median | Mode | Range |
|---|----------------|------------|--------|--------------|-------|
| 1 | 45,48,49,51,52,53,55,57,57,57,60,60,61,65 | 55.14 | 56 | 57 | 20 |
| 2 | 110,110,112,113,113,115,115,115,121,121,123,124,129 | 117 | 115 | 115 | 19 |
| 3 | 2,4,4,7,7,7,8,8,9,11,11,11,12,12,14,15 | 8.875 | 8.5 | 7 and 11 | 13 |
| 4 | 76,77,77,77,77,79,81,81,81,83,83,85,87,91 | 81.07 | 81 | 77 | 15 |
| 5 | 0.2,0.2,0.2,0.3,0.4,0.6,0.7,0.7,0.9,1.1,1.1,1.2,1.5 | 0.7 | 0.7 | 0.2 | 1.3 |
| 6 | 4.5,4.7,4.9,5.1,5.1,5.4,5.6,5.7,6.2,6.2,6.2,6.4 | 5.5 | 5.5 | 6.2 | 1.9 |

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