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: Write the step-deviation relation in fraction form.
\[ \bar{u} = \frac{\bar{x}-a}{h} \] With $\bar{x}=64$, $a=62.5=\frac{125}{2}$, and $h=5$, keep everything as fractions instead of decimals.
Step 2: Compute the numerator as a fraction. \[ \bar{x} - a = 64 - \frac{125}{2} = \frac{128-125}{2} = \frac{3}{2} \]
Step 3: Divide by h and simplify. \[ \bar{u} = \frac{3/2}{5} = \frac{3}{10} = 0.3 \]
\[ \boxed{\bar{u} = 0.3} \]