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

To solve this problem, we will use the formula for the mean of a grouped frequency distribution using the step-deviation method. The formula is given by:

\(\bar{x} = a + \bar{u} \times h\)

We need to find the value of \(\bar{u}\).

1. Given the values:
   • \(\bar{x} = 64\)
   • \(h = 5\)
   • \(a = 62.5\)
2. Substitute these values into the formula:

\(64 = 62.5 + \bar{u} \times 5\)

1. Rearrange the equation to solve for \(\bar{u}\):

\(64 - 62.5 = \bar{u} \times 5\)

\(1.5 = \bar{u} \times 5\)

1. Divide both sides by 5 to isolate \(\bar{u}\):

\(\bar{u} = \frac{1.5}{5}\)

\(\bar{u} = 0.3\)

Therefore, the value of \(\bar{u}\) is \(0.3\).

The correct answer is \(0.3\).