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

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1

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

1. Order: First, we arrange the numbers from smallest to largest.
$45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65$

2. Mean (Average): Add all the numbers together and divide by how many numbers there are (14).
* Sum: $45+48+49+51+52+53+55+57+57+57+60+60+61+65 = 770$
* Mean: $770 \div 14 = \mathbf{55}$

3. Median (Middle): Since there are 14 numbers (an even amount), the median is the average of the two middle numbers (the 7th and 8th numbers).
* The 7th number is 55.
* The 8th number is 57.
* Median: $(55 + 57) \div 2 = \mathbf{56}$

4. Mode (Most Frequent): Look for the number that appears most often.
* 57 appears three times. No other number appears more than twice.
* Mode: $\mathbf{57}$

5. Range: Subtract the smallest number from the largest number.
* Range: $65 - 45 = \mathbf{20}$

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Problem 2

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

1. Order:
$110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129$

2. Mean: There are 13 numbers.
* Sum: $1511$
* Mean: $1511 \div 13 \approx \mathbf{116.23}$ (rounded to two decimal places)

3. Median: The middle number in a list of 13 is the 7th number.
* Median: $\mathbf{115}$

4. Mode:
* 115 appears three times.
* Mode: $\mathbf{115}$

5. Range:
* Range: $129 - 110 = \mathbf{19}$

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Problem 3

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

1. Order: Be careful with negative numbers; they go first.
$-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15$

2. Mean: There are 16 numbers.
* Sum: $48$
* Mean: $48 \div 16 = \mathbf{3}$

3. Median: The middle two numbers are the 8th and 9th numbers.
* 8th number: 4
* 9th number: 4
* Median: $(4 + 4) \div 2 = \mathbf{4}$

4. Mode:
* Both 4 and 7 appear three times.
* Mode: $\mathbf{4 \text{ and } 7}$

5. Range: Largest minus Smallest.
* Range: $15 - (-8) = 15 + 8 = \mathbf{23}$

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Problem 4

Data: $\{83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77\}$

1. Order:
$72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91$

2. Mean: There are 15 numbers.
* Sum: $1200$
* Mean: $1200 \div 15 = \mathbf{80}$

3. Median: The middle number (8th number).
* Median: $\mathbf{81}$

4. Mode:
* 77 appears four times.
* Mode: $\mathbf{77}$

5. Range:
* Range: $91 - 72 = \mathbf{19}$

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Problem 5

Data: $\{0.7, 0.2, 0.9, 1.2, 1.5, 0.4, 0.6, 0.2, 1.1, 0.3, 0.7, 0.2, 1.1\}$

1. Order:
$0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5$

2. Mean: There are 13 numbers.
* Sum: $9.1$
* Mean: $9.1 \div 13 = \mathbf{0.7}$

3. Median: The middle number (7th number).
* Median: $\mathbf{0.7}$

4. Mode:
* 0.2 appears three times.
* Mode: $\mathbf{0.2}$

5. Range:
* Range: $1.5 - 0.2 = \mathbf{1.3}$

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Problem 6

Data: $\{6.2, 5.6, 4.9, 5.1, 6.2, 5.7, 5.1, 4.7, 5.4, 6.2, 4.5, 6.4\}$

1. Order:
$4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4$

2. Mean: There are 12 numbers.
* Sum: $66$
* Mean: $66 \div 12 = \mathbf{5.5}$

3. Median: Average of the 6th and 7th numbers.
* 6th number: 5.4
* 7th number: 5.6
* Median: $(5.4 + 5.6) \div 2 = \mathbf{5.5}$

4. Mode:
* 6.2 appears three times.
* Mode: $\mathbf{6.2}$

5. Range:
* Range: $6.4 - 4.5 = \mathbf{1.9}$

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Final Answer:

1)
* Order: 45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65
* Mean: 55
* Median: 56
* Mode: 57
* Range: 20

2)
* Order: 110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129
* Mean: 116.23
* Median: 115
* Mode: 115
* Range: 19

3)
* Order: -8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15
* Mean: 3
* Median: 4
* Mode: 4 and 7
* Range: 23

4)
* Order: 72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91
* Mean: 80
* Median: 81
* Mode: 77
* Range: 19

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

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