Question

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x - a}{h} = u\right)$. It was found that $\bar{x} = 64$, $h = 5$ and $a = 62.5$. The value of $\bar{u}$ is

• A. $0.5$
• B. $1.5$
• C. $0.3$
• D. $7.5$

Hint:

Double check your linear arithmetic: subtracting $62.5$ from $64$ gives $1.5$, and dividing $1.5$ by $5$ is equivalent to dividing $15$ by $50$, which is easily simplified to $0.3$.

Answer 1

The Correct Option is C

Step 1: Recall the step-deviation mean formula.
\[ \bar x = a + h\bar u \]
Step 2: Find how far the mean is from the assumed mean.
\[ \bar x - a = 64 - 62.5 = 1.5 \]
Step 3: Divide by the class width to get $\bar u$.
\[ \bar u = \frac{1.5}{5} = 0.3 \]
Step 4: Conclude.
This matches option (3).
\[ \boxed{0.3} \]