In the formula `bar(x)=a+h(sumf_(i)u_(i))/(sumf_(i))`
for finding the mean of grouped frequency distribution `u_(i)` is equal to

Options

A. `(x_(i)+a)/(h)`
B. `h(x_(i)-a)`
C. `(x_(i)-a)/(h)`
D. `(a-x_(i))/(h)`

Explanation

To solve the question regarding the formula for finding the mean of a grouped frequency distribution, we need to identify what \( u_i \) represents in the formula:

\[ \bar{x} = a + h \left( \frac{\sum f_i u_i}{\sum f_i} \right) \]

### Step-by-Step Solution:

1. **Understanding the Components of the Formula:**
- In the formula, \( \bar{x} \) represents the mean of the grouped frequency distribution.
- \( a \) is the assumed mean.
- \( h \) is the class width (the difference between the upper and lower boundaries of the class intervals).
- \( f_i \) represents the frequency of the \( i^{th} \) class.
- \( u_i \) is a term that we need to define.

2. **Identifying \( u_i \):**
- The term \( u_i \) is defined as the deviation of the mid-point of the class interval from the assumed mean, normalized by the class width.
- Mathematically, it is expressed as:
\[ u_i = \frac{x_i - a}{h} \]
where \( x_i \) is the mid-point of the \( i^{th} \) class.

3. **Conclusion:**
- Therefore, in the context of the formula provided, \( u_i \) is equal to:
\[ u_i = \frac{x_i - a}{h} \]

### Final Answer:
Thus, the value of \( u_i \) in the formula is:
\[ u_i = \frac{x_i - a}{h} \]