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: Convert the given decimals to fractions first.
$\bar{x} - a = 64 - 62.5 = 1.5 = \frac{3}{2}$.
Step 2: Use the step-deviation relation.
Since $\bar{x} = a + h\bar{u}$, we get $\bar{u} = \frac{\bar{x}-a}{h} = \frac{3/2}{5}$.
Step 3: Simplify the fraction.
$\frac{3/2}{5} = \frac{3}{10} = 0.3$, avoiding any decimal rounding along the way.
\[ \boxed{\bar{u} = 0.3} \]