A Chapter 9: Mcasures of Varlation section Exerclses $$ 9,4 $$ Exerclse 10 Describe and correct the error in finding the range of the data. The range is the middle number. The range is 41 . The data were not ordered from least to greatest. $$ 35,38,41,44,48,49,51 $$. $$ 48,51,41,35,44,38 $$ The range is the middle number, 44 . The range is the largest number in a data set. The range is 51 . The data were not ordered from least to greatest. $$ 35,38,41,44,48,49,51 $$, or 11 . The least value is 35 This greatest value is 51 . The range is $$ 51-35 $$, o 16 . The

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A> Chapter 9: Mcasures of Varlation > section Exerclses $$ 9,4> $$ Exerclse 10 Describe and correct the error in finding the range of the data. The range is the middle number. The range is 41 . The data were not ordered from least to greatest. $$ 35,38,41,44,48,49,51 $$. $$ 48,51,41,35,44,38 $$ The range is the middle number, 44 . The range is the largest number in a data set. The range is 51 . The data were not ordered from least to greatest. $$ 35,38,41,44,48,49,51 $$, or 11 . The least value is 35 This greatest value is 51 . The range is $$ 51-35 $$, o 16 . The

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To address the problem, let's break down the statements and identify the errors in finding the range of the data.

### Known Conditions:
1. The data set provided is $$ 35, 38, 41, 44, 48, 49, 51 $$.
2. The data set is also presented in a different order: $$ 48, 51, 41, 35, 44, 38 $$.
3. The range is incorrectly defined in several ways in the statements.

### Step-by-Step Analysis:

1. **Definition of Range**:
   - The range of a data set is defined as the difference between the largest and smallest values in the set. It is calculated as:
     $$
     \text{Range} = \text{Maximum} - \text{Minimum}
     $$

2. **Identifying the Maximum and Minimum**:
   - From the ordered data set $$ 35, 38, 41, 44, 48, 49, 51 $$:
     - The **minimum** value is $$ 35 $$.
     - The **maximum** value is $$ 51 $$.

3. **Calculating the Range**:
   - Using the formula for range:
     $$
     \text{Range} = 51 - 35
     $$

4. **Performing the Calculation**:
   - Now, let's calculate the range:
     $$
     \text{Range} = 51 - 35 = 16
     $$

### Errors Identified:
1. **Misdefinition of Range**:
   - The statement "The range is the middle number" is incorrect. The range is not the middle number; it is the difference between the largest and smallest numbers.

2. **Incorrect Calculation**:
   - The statement "The range is 41" is incorrect because it does not follow the correct definition of range.

3. **Confusion in Data Ordering**:
   - The data must be ordered to correctly identify the minimum and maximum values. The second set of data $$ 48, 51, 41, 35, 44, 38 $$ is not ordered, which can lead to confusion.

4. **Final Calculation Error**:
   - The statement "The range is $$ 51 - 35 $$, or 16" is correct, but it was preceded by incorrect definitions and calculations.

### Conclusion:
The correct range of the data set $$ 35, 38, 41, 44, 48, 49, 51 $$ is $$ 16 $$. The errors stem from misunderstanding the definition of range and not ordering the data correctly. The correct approach is to identify the minimum and maximum values and then calculate the range as the difference between them.
The range of the data set is 16.

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