Question

Calculate the arithmetic mean (approximately) from the following data

• A. \(31.63\)
• B. \(30.57\)
• C. \(32.57\)
• D. \(31.65\)

Hint:

For grouped data, \[ \boxed{ \bar{x}=\frac{\sum fx_i}{\sum f} } \] where \(x_i\) is the class mark (midpoint of each class interval).

Answer 1

The Correct Option is C

Step 1: Find the class marks. \[ \begin{array}{|c|c|c|} \hline \text{Class} & f & x_i \hline 0-10 & 2 & 5 10-20 & 8 & 15 20-30 & 15 & 25 30-40 & 25 & 35 40-50 & 20 & 45 \hline \end{array} \]

Step 2: Calculate \(fx_i\). \[ \begin{array}{|c|c|} \hline f & fx_i \hline 2 & 10 8 & 120 15 & 375 25 & 875 20 & 900 \hline \end{array} \] \[ \sum f=70,\qquad \sum fx_i=2280. \]

Step 3: Find the arithmetic mean. \[ \bar{x} = \frac{\sum fx_i}{\sum f} = \frac{2280}{70} = 32.57. \]

Step 4: Final conclusion. \[ \boxed{\bar{x}\approx 32.57} \] Hence, the correct option is \(\boxed{(C)}\).