A set of data contains 64 as the highest value and its range is 13, the lowest value of the data is______.

Answer

To find the lowest value of the data set, we can follow these steps:

### Step 1: Understand the concept of range
The range of a data set is defined as the difference between the highest value and the lowest value. Mathematically, it can be expressed as:
\[ \text{Range} = \text{Highest Value} - \text{Lowest Value} \]

### Step 2: Identify the given values
From the problem, we know:
- Highest Value = 64
- Range = 13

### Step 3: Set up the equation
Using the formula for range, we can rearrange it to find the lowest value:
\[ \text{Lowest Value} = \text{Highest Value} - \text{Range} \]

### Step 4: Substitute the known values into the equation
Now, we substitute the values we have into the equation:
\[ \text{Lowest Value} = 64 - 13 \]

### Step 5: Perform the calculation
Now we perform the subtraction:
\[ \text{Lowest Value} = 64 - 13 = 51 \]

### Final Answer
The lowest value of the data set is **51**.

---