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: Understanding the Question:
We are given statistical values obtained while calculating the mean of a grouped frequency distribution using the step-deviation method.
The given parameters are: mean $\bar{x} = 64$, class size $h = 5$, and assumed mean $a = 62.5$.
We need to calculate the mean of the step deviations, represented by $\bar{u}$.

Step 2: Key Formula or Approach:
The formula for calculating the mean of a grouped frequency distribution by the step-deviation method is:
\[ \bar{x} = a + h\bar{u} \]
We can rearrange this formula to isolate and solve for $\bar{u}$:
\[ \bar{u} = \frac{\bar{x} - a}{h} \]

Step 3: Detailed Explanation:

• Start with the standard step-deviation mean formula:
\[ \bar{x} = a + h\bar{u} \]

• Substitute the given values ($\bar{x} = 64$, $a = 62.5$, and $h = 5$) into the equation:
\[ 64 = 62.5 + 5\bar{u} \]

• Subtract the assumed mean ($62.5$) from both sides to isolate the term with $\bar{u}$:
\[ 64 - 62.5 = 5\bar{u} \]
\[ 1.5 = 5\bar{u} \]

• Divide both sides by the class size ($5$) to solve for $\bar{u}$:
\[ \bar{u} = \frac{1.5}{5} \]

• Simplify the decimal division:
\[ \bar{u} = \frac{15}{50} = \frac{3}{10} = 0.3 \]


Step 4: Final Answer:
The value of $\bar{u}$ is $0.3$.