The mean of the following data is
{("Class interval",f),(" "10-15,5),(" "15-20,7),(" "20-25,3),(" "25-30,4),(" "30-35,8):}

Options

A. 22
B. 23.05
C. 24.05
D. 27.05

Explanation

To find the mean of the given data, we will follow these steps:

### Step 1: Identify the class intervals and their corresponding frequencies.
The data provided is:
- Class intervals: 10-15, 15-20, 20-25, 25-30, 30-35
- Frequencies (f): 5, 7, 3, 4, 8

### Step 2: Calculate the midpoints (x_i) for each class interval.
The midpoint (x_i) for each class interval is calculated as:
\[ x_i = \frac{\text{Lower limit} + \text{Upper limit}}{2} \]

Calculating midpoints:
- For 10-15: \( x_1 = \frac{10 + 15}{2} = 12.5 \)
- For 15-20: \( x_2 = \frac{15 + 20}{2} = 17.5 \)
- For 20-25: \( x_3 = \frac{20 + 25}{2} = 22.5 \)
- For 25-30: \( x_4 = \frac{25 + 30}{2} = 27.5 \)
- For 30-35: \( x_5 = \frac{30 + 35}{2} = 32.5 \)

### Step 3: Create a table to calculate \( f_i \) and \( x_i \cdot f_i \).
| Class Interval | Frequency (f) | Midpoint (x_i) | \( f_i \cdot x_i \) |
|----------------|---------------|----------------|----------------------|
| 10 - 15 | 5 | 12.5 | \( 5 \cdot 12.5 = 62.5 \) |
| 15 - 20 | 7 | 17.5 | \( 7 \cdot 17.5 = 122.5 \) |
| 20 - 25 | 3 | 22.5 | \( 3 \cdot 22.5 = 67.5 \) |
| 25 - 30 | 4 | 27.5 | \( 4 \cdot 27.5 = 110 \) |
| 30 - 35 | 8 | 32.5 | \( 8 \cdot 32.5 = 260 \) |

### Step 4: Calculate the total of frequencies and the total of \( f_i \cdot x_i \).
- Total frequency \( \sum f_i = 5 + 7 + 3 + 4 + 8 = 27 \)
- Total \( \sum (f_i \cdot x_i) = 62.5 + 122.5 + 67.5 + 110 + 260 = 622.5 \)

### Step 5: Calculate the mean using the formula.
The mean is given by the formula:
\[ \text{Mean} = \frac{\sum (f_i \cdot x_i)}{\sum f_i} \]
Substituting the values:
\[ \text{Mean} = \frac{622.5}{27} \approx 23.05 \]

### Final Answer:
The mean of the given data is approximately **23.05**.

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