Worksheet for finding mean, median, mode, and range of given data sets.

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

1. Order the numbers from smallest to largest.
2. Calculate the mean (average): sum of all values divided by number of values.
3. Find the median: middle value when ordered (or average of two middle values if even count).
4. Determine the mode: most frequent value(s). If no repeats, there is no mode.
5. Compute the range: difference between largest and smallest values.

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Problem 1)

Data: {61, 57, 49, 60, 45, 51, 57, 60, 53, 57, 55, 48, 65, 52}

#### Step 1: 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 compute:
- 45+48=93
- +49=142
- +51=193
- +52=245
- +53=300
- +55=355
- +57=412
- +57=469
- +57=526
- +60=586
- +60=646
- +61=707
- +65=772

Number of values = 14
Mean = 772 ÷ 14 ≈ 55.14

#### Step 3: Median
Ordered list has 14 values → 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, others appear ≤2 times
→ Mode = 57

#### Step 5: Range
Largest = 65, Smallest = 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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Problem 2)

Data: {129, 113, 110, 123, 112, 115, 110, 124, 121, 113, 115, 121, 115}

#### Step 1: Order
{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

Count = 13
Mean = 1521 ÷ 13 = 117

#### Step 3: Median
13 values → 7th value is median
7th value = 115

#### Step 4: Mode
115 appears 3 times, others: 110(2), 113(2), 121(2), etc.
→ 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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Problem 3)

Data: {-4, 7, 4, -8, 13, 4, -2, -5, 7, -6, 5, 15, -2, 1, 12, 7}

#### Step 1: Order
{-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15}

#### Step 2: Mean
Sum = -8 + (-6) = -14
+(-5)= -19
+(-4)= -23
+(-2)= -25
+(-2)= -27
+1= -26
+4= -22
+4= -18
+5= -13
+7= -6
+7= 1
+7= 8
+12= 20
+13= 33
+15= 48

Count = 16
Mean = 48 ÷ 16 = 3

#### Step 3: Median
16 values → average of 8th and 9th
- 8th = 4
- 9th = 4
Median = (4+4)/2 = 4

#### Step 4: Mode
7 appears 3 times, 4 appears 2 times, -2 appears 2 times → Most frequent is 7
→ Mode = 7

#### Step 5: Range
Max = 15, Min = -8
Range = 15 - (-8) = 15 + 8 = 23

✔ Answer 3:
- Order: {-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15}
- Mean: 3
- Median: 4
- Mode: 7
- Range: 23

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Problem 4)

Data: {83, 77, 81, 79, 85, 77, 76, 87, 81, 83, 77, 91, 81, 77}

#### Step 1: Order
{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

Count = 14
Mean = 1135 ÷ 14 ≈ 81.07

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

#### Step 4: Mode
77 appears 4 times, 81 appears 3 times, others less → 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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Problem 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
{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

Count = 13
Mean = 9.1 ÷ 13 ≈ 0.7

#### Step 3: Median
13 values → 7th value = 0.7

#### Step 4: Mode
0.2 appears 3 times, 1.1 appears 2 times, 0.7 appears 2 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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Problem 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
{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

Count = 12
Mean = 66.0 ÷ 12 = 5.5

#### Step 3: Median
12 values → 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, 5.1 appears 2 times, others once → 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:

| Problem | Mean | Median | Mode | Range |
|--------|----------|--------|--------|-------|
| 1 | 55.14 | 56 | 57 | 20 |
| 2 | 117 | 115 | 115 | 19 |
| 3 | 3 | 4 | 7 | 23 |
| 4 | 81.07 | 81 | 77 | 15 |
| 5 | 0.7 | 0.7 | 0.2 | 1.3 |
| 6 | 5.5 | 5.5 | 6.2 | 1.9 |

You can now fill in the worksheet accordingly! Let me know if you want it formatted for printing or need explanations on any concept.