Worksheet for calculating mean, median, mode, and range from given data sets.

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

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

Step 1: Order the data
First, we list the numbers from smallest to largest.
Order: {45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65}

Step 2: Find the Mean
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: $770 \div 14 = \mathbf{55}$

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

Step 4: Find the Mode
The mode is the number that appears most often.
57 appears three times. No other number appears more than twice.
Mode: 57

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

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

Step 1: Order the data
Order: {110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129}

Step 2: Find the Mean
There are 13 numbers.
Sum: $110+110+112+113+113+115+115+115+121+121+123+124+129 = 1521$
Mean: $1521 \div 13 = \mathbf{117}$

Step 3: Find the Median
With 13 numbers, the median is the exact middle one (the 7th number).
Median: 115

Step 4: Find the Mode
115 appears three times. 110, 113, and 121 appear twice.
Mode: 115

Step 5: Find the Range
Range: $129 - 110 = \mathbf{19}$

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

Step 1: Order the data
Be careful with the negative signs! Smallest means furthest to the left on a number line.
Order: {-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15}

Step 2: Find the Mean
There are 16 numbers.
Sum: $(-8-6-5-4-2-2) + (1+4+4+5+7+7+7+12+13+15)$
Sum of negatives: -27
Sum of positives: 75
Total Sum: $75 - 27 = 48$
Mean: $48 \div 16 = \mathbf{3}$

Step 3: Find the Median
With 16 numbers, we average the 8th and 9th numbers.
8th number: 4
9th number: 4
Median: $(4 + 4) \div 2 = \mathbf{4}$

Step 4: Find the Mode
7 appears three times. 4 and -2 appear twice.
Mode: 7

Step 5: Find the Range
Largest minus Smallest: $15 - (-8)$. Subtracting a negative is like adding.
Range: $15 + 8 = \mathbf{23}$

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4) Data Set: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77}

Step 1: Order the data
Order: {72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91}

Step 2: Find the Mean
There are 15 numbers.
Sum: $72+76+77+77+77+77+79+81+81+81+83+83+85+87+91 = 1207$
Mean: $1207 \div 15 = \mathbf{80.46...}$ (Rounded to two decimal places: 80.47)

Step 3: Find the Median
With 15 numbers, the median is the 8th number.
Median: 81

Step 4: Find the Mode
77 appears four times. 81 appears three times.
Mode: 77

Step 5: Find the Range
Range: $91 - 72 = \mathbf{19}$

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5) Data Set: {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 the data
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: Find the Mean
There are 13 numbers.
Sum: $0.2+0.2+0.2+0.3+0.4+0.6+0.7+0.7+0.9+1.1+1.1+1.2+1.5 = 9.1$
Mean: $9.1 \div 13 = \mathbf{0.7}$

Step 3: Find the Median
The middle number (7th number) is 0.7.
Median: 0.7

Step 4: Find the Mode
0.2 appears three times.
Mode: 0.2

Step 5: Find the Range
Range: $1.5 - 0.2 = \mathbf{1.3}$

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6) Data Set: {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 the data
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: Find the Mean
There are 12 numbers.
Sum: $4.5+4.7+4.9+5.1+5.1+5.4+5.6+5.7+6.2+6.2+6.2+6.4 = 66$
Mean: $66 \div 12 = \mathbf{5.5}$

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

Step 4: Find the Mode
6.2 appears three times.
Mode: 6.2

Step 5: Find the 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: 117
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: 7
Range: 23

4)
Order: {72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91}
Mean: 80.47 (approx)
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