Question

Find the range of the data set.
8 and four sevenths comma
11 and four sevenths comma
8 and one seventh comma
10 and three sevenths comma
17 comma
11 and one seventh comma
8 and three sevenths
Question content area bottom
Part 1
The range is
  
enter your response here.
​(Type an​ integer, proper​ fraction, or mixed​ number.)

Answer 1

To find the range of a data set, you subtract the minimum value from the maximum value.

Here's the data set you've provided:

1. \( 8 \frac{4}{7} \)
2. \( 11 \frac{4}{7} \)
3. \( 8 \frac{1}{7} \)
4. \( 10 \frac{3}{7} \)
5. \( 17 \)
6. \( 11 \frac{1}{7} \)
7. \( 8 \frac{3}{7} \)

**Step 1: Convert mixed numbers to improper fractions for easier comparison (optional).**

- \( 8 \frac{4}{7} = \frac{60}{7} \)
- \( 11 \frac{4}{7} = \frac{81}{7} \)
- \( 8 \frac{1}{7} = \frac{57}{7} \)
- \( 10 \frac{3}{7} = \frac{75}{7} \)
- \( 17 = \frac{119}{7} \)
- \( 11 \frac{1}{7} = \frac{78}{7} \)
- \( 8 \frac{3}{7} = \frac{59}{7} \)

**Step 2: Identify the minimum and maximum values.**

From the original data:
- The minimum value is \( 8 \frac{1}{7} \) (or \( 57/7 \)).
- The maximum value is \( 17 \) (or \( 17/1 \)).

**Step 3: Calculate the range.**

\[
\text{Range} = \text{Maximum} - \text{Minimum} = 17 - 8 \frac{1}{7}
\]

To subtract, convert \( 8 \frac{1}{7} \) to an improper fraction:

\[
8 \frac{1}{7} = \frac{57}{7}
\]

Convert \( 17 \) to a fraction with a denominator of 7:

\[
17 = \frac{119}{7}
\]

Perform the subtraction:

\[
\text{Range} = \frac{119}{7} - \frac{57}{7} = \frac{119 - 57}{7} = \frac{62}{7}
\]

**Step 4: Convert \( \frac{62}{7} \) to a mixed number.**

To convert \( \frac{62}{7} \), divide 62 by 7:

\[
62 \div 7 = 8 \quad \text{(whole number)}
\]
\[
62 - (7 \times 8) = 6 \quad \text{(remainder)}
\]

So,

\[
\frac{62}{7} = 8 \frac{6}{7}
\]

**Final Answer:**

The range of the data set is \( 8 \frac{6}{7} \).