The frequency distribution for x is an given below. What is the range of f? `
`{:(x,f),(0,1),(1,5),(2,4),(3,4):}`

Options

A. 0
B. 1
C. 3
D. 4

Answer

To find the range of the frequency distribution given by the pairs \((x, f)\), we will follow these steps:

1. **Identify the values of f**: From the frequency distribution, we have the following values of f:
- For \(x = 0\), \(f = 1\)
- For \(x = 1\), \(f = 5\)
- For \(x = 2\), \(f = 4\)
- For \(x = 3\), \(f = 4\)

Therefore, the values of f are: \(1, 5, 4, 4\).

2. **Determine the maximum value of f**: The maximum value from the set of f values is:
\[ \text{Maximum of f} = 5 \]

3. **Determine the minimum value of f**: The minimum value from the set of f values is:
\[ \text{Minimum of f} = 1 \]

4. **Calculate the range of f**: The range is calculated using the formula:
\[ \text{Range} = \text{Maximum} - \text{Minimum} \]
Substituting the values we found:
\[ \text{Range} = 5 - 1 = 4 \]

Thus, the range of f is \(4\).