The mid-value of a class interval is 25 and the class size is 8. The class interval is

Options

A. 37 - 45
B. 21 - 29
C. 36.5 - 44.5
D. 36.5 - 46.5

Answer

To find the class interval given the mid-value and class size, we can follow these steps:

### Step 1: Understand the given information
We are given:
- Mid-value (M) = 25
- Class size (C) = 8

### Step 2: Set up the equations
The mid-value of a class interval can be expressed as:
\[ M = \frac{a + b}{2} \]
where \( a \) is the lower limit and \( b \) is the upper limit of the class interval.

The class size is defined as:
\[ C = b - a \]

### Step 3: Substitute the known values
From the mid-value equation:
\[ 25 = \frac{a + b}{2} \]
Multiplying both sides by 2 gives:
\[ a + b = 50 \] (Equation 1)

From the class size equation:
\[ 8 = b - a \] (Equation 2)

### Step 4: Solve the equations
Now we have two equations:
1. \( a + b = 50 \)
2. \( b - a = 8 \)

We can solve these equations simultaneously.

From Equation 2, we can express \( b \) in terms of \( a \):
\[ b = a + 8 \]

### Step 5: Substitute \( b \) into Equation 1
Substituting \( b = a + 8 \) into Equation 1:
\[ a + (a + 8) = 50 \]
\[ 2a + 8 = 50 \]

### Step 6: Solve for \( a \)
Subtract 8 from both sides:
\[ 2a = 42 \]
Now divide by 2:
\[ a = 21 \]

### Step 7: Find \( b \)
Now substitute \( a = 21 \) back into the equation for \( b \):
\[ b = 21 + 8 = 29 \]

### Step 8: Write the class interval
The class interval is given by the lower limit \( a \) and the upper limit \( b \):
\[ \text{Class Interval} = [21, 29] \]

### Final Answer
The class interval is **[21, 29]**.

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