If `u_(i)=(x_(i)-25)/(10), sumf_(i)u_(i)=20,sumf_(i)=100` then `overline(x)=`

Options

A. 23
B. 24
C. 27
D. 25

Answer

To solve the problem step by step, we will use the information provided in the question and the formula for calculating the mean.

### Step 1: Understand the given information
We have:
- \( u_i = \frac{x_i - 25}{10} \)
- \( \sum f_i u_i = 20 \)
- \( \sum f_i = 100 \)

### Step 2: Identify the values of \( A \) and \( H \)
From the formula for \( u_i \), we can identify:
- \( A = 25 \) (the constant subtracted from \( x_i \))
- \( H = 10 \) (the constant by which \( x_i \) is divided)

### Step 3: Use the formula for the mean
The formula for the mean \( \overline{x} \) in terms of \( A \), \( H \), and the summations is given by:
\[ \overline{x} = A + H \cdot \frac{\sum f_i u_i}{\sum f_i} \]

### Step 4: Substitute the known values into the formula
Now, substituting the values we have:
- \( A = 25 \)
- \( H = 10 \)
- \( \sum f_i u_i = 20 \)
- \( \sum f_i = 100 \)

We can substitute these into the formula:
\[ \overline{x} = 25 + 10 \cdot \frac{20}{100} \]

### Step 5: Simplify the expression
First, calculate \( \frac{20}{100} \):
\[ \frac{20}{100} = 0.2 \]
Now, multiply by \( H \):
\[ 10 \cdot 0.2 = 2 \]
Finally, add this to \( A \):
\[ \overline{x} = 25 + 2 = 27 \]

### Final Answer
Thus, the mean \( \overline{x} \) is:
\[ \overline{x} = 27 \]