Question

While calculating mean of a grouped frequency distribution, step deviation method was used \(u = \frac{x-a}{h}\). 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:

Always ensure that the units of \((x-a)\) match \(h \bar{u}\). Here, the difference \(1.5\) is less than \(h=5\), so \(\bar{u}\) must be a decimal less than \(1\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The step deviation method simplifies the calculation of the mean for grouped data. The mean \(\bar{x}\) is related to the mean of deviations \(\bar{u}\).
Step 2: Key Formula or Approach:
The formula for the mean in the step-deviation method is:
\[ \bar{x} = a + h \bar{u} \]
Step 3: Detailed Explanation:
Given:
\(\bar{x} = 64\)
\(a = 62.5\)
\(h = 5\)
Substitute these into the formula:
\[ 64 = 62.5 + 5\bar{u} \]
\[ 64 - 62.5 = 5\bar{u} \]
\[ 1.5 = 5\bar{u} \]
\[ \bar{u} = \frac{1.5}{5} = 0.3 \]
Step 4: Final Answer:
The value of \(\bar{u}\) is \(0.3\).