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

To solve the problem of finding the mean, median, mode, and range for each set of numbers, we will go through each set step by step. Let's break it down:

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Step 1: Definitions

- Mean: The average of the numbers. It is calculated as:
$$
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
$$
- Median: The middle value when the numbers are arranged in ascending order. If there is an even number of values, the median is the average of the two middle numbers.
- Mode: The number that appears most frequently. If no number repeats, there is no mode.
- Range: The difference between the largest and smallest numbers:
$$
\text{Range} = \text{Largest number} - \text{Smallest number}
$$

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Step 2: Solve Each Set

#### Set 1: {7.5, 8.3, 9.5, 8.3, 7.5}
1. Mean:
$$
\text{Mean} = \frac{7.5 + 8.3 + 9.5 + 8.3 + 7.5}{5} = \frac{41.1}{5} = 8.22
$$
2. Median:
Arrange in ascending order: {7.5, 7.5, 8.3, 8.3, 9.5}
The middle value is the third number: 8.3
3. Mode:
The number that appears most frequently is 8.3 (appears twice).
4. Range:
$$
\text{Range} = 9.5 - 7.5 = 2.0
$$

Answer for Set 1:
$$
\text{Mean} = 8.22, \quad \text{Median} = 8.3, \quad \text{Mode} = 8.3, \quad \text{Range} = 2.0
$$

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#### Set 2: {36.8, 36.8, 36.8, 36.8, 36.8}
1. Mean:
$$
\text{Mean} = \frac{36.8 + 36.8 + 36.8 + 36.8 + 36.8}{5} = \frac{184.0}{5} = 36.8
$$
2. Median:
All numbers are the same: {36.8, 36.8, 36.8, 36.8, 36.8}
The middle value is 36.8.
3. Mode:
The number that appears most frequently is 36.8 (appears five times).
4. Range:
$$
\text{Range} = 36.8 - 36.8 = 0.0
$$

Answer for Set 2:
$$
\text{Mean} = 36.8, \quad \text{Median} = 36.8, \quad \text{Mode} = 36.8, \quad \text{Range} = 0.0
$$

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#### Set 3: {52.19, 49.19, 48.52, 52.33, 49.23}
1. Mean:
$$
\text{Mean} = \frac{52.19 + 49.19 + 48.52 + 52.33 + 49.23}{5} = \frac{251.46}{5} = 50.292
$$
2. Median:
Arrange in ascending order: {48.52, 49.19, 49.23, 52.19, 52.33}
The middle value is the third number: 49.23
3. Mode:
No number repeats, so there is no mode.
4. Range:
$$
\text{Range} = 52.33 - 48.52 = 3.81
$$

Answer for Set 3:
$$
\text{Mean} = 50.292, \quad \text{Median} = 49.23, \quad \text{Mode} = \text{No mode}, \quad \text{Range} = 3.81
$$

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#### Set 4: {98.04, 77.7, 98.04, 88.79, 88.79}
1. Mean:
$$
\text{Mean} = \frac{98.04 + 77.7 + 98.04 + 88.79 + 88.79}{5} = \frac{451.36}{5} = 90.272
$$
2. Median:
Arrange in ascending order: {77.7, 88.79, 88.79, 98.04, 98.04}
The middle value is the third number: 88.79
3. Mode:
The numbers 88.79 and 98.04 both appear twice, so there are two modes: 88.79 and 98.04.
4. Range:
$$
\text{Range} = 98.04 - 77.7 = 20.34
$$

Answer for Set 4:
$$
\text{Mean} = 90.272, \quad \text{Median} = 88.79, \quad \text{Mode} = 88.79, 98.04, \quad \text{Range} = 20.34
$$

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#### Set 5: {25.33, 26.43, 26.43, 26.52, 26.67}
1. Mean:
$$
\text{Mean} = \frac{25.33 + 26.43 + 26.43 + 26.52 + 26.67}{5} = \frac{131.38}{5} = 26.276
$$
2. Median:
Arrange in ascending order: {25.33, 26.43, 26.43, 26.52, 26.67}
The middle value is the third number: 26.43
3. Mode:
The number that appears most frequently is 26.43 (appears twice).
4. Range:
$$
\text{Range} = 26.67 - 25.33 = 1.34
$$

Answer for Set 5:
$$
\text{Mean} = 26.276, \quad \text{Median} = 26.43, \quad \text{Mode} = 26.43, \quad \text{Range} = 1.34
$$

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#### Set 6: {11.25, 18.86, 18.86, 17.78, 18.86, 18.86, 18.86, 18.86}
1. Mean:
$$
\text{Mean} = \frac{11.25 + 18.86 + 18.86 + 17.78 + 18.86 + 18.86 + 18.86 + 18.86}{8} = \frac{144.25}{8} = 18.03125
$$
2. Median:
Arrange in ascending order: {11.25, 17.78, 18.86, 18.86, 18.86, 18.86, 18.86, 18.86}
The middle values are the fourth and fifth numbers: 18.86 and 18.86
$$
\text{Median} = \frac{18.86 + 18.86}{2} = 18.86
$$
3. Mode:
The number that appears most frequently is 18.86 (appears six times).
4. Range:
$$
\text{Range} = 18.86 - 11.25 = 7.61
$$

Answer for Set 6:
$$
\text{Mean} = 18.03125, \quad \text{Median} = 18.86, \quad \text{Mode} = 18.86, \quad \text{Range} = 7.61
$$

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Final Answers

1. $\boxed{8.22, 8.3, 8.3, 2.0}$
2. $\boxed{36.8, 36.8, 36.8, 0.0}$
3. $\boxed{50.292, 49.23, \text{No mode}, 3.81}$
4. $\boxed{90.272, 88.79, 88.79, 98.04, 20.34}$
5. $\boxed{26.276, 26.43, 26.43, 1.34}$
6. $\boxed{18.03125, 18.86, 18.86, 7.61}$