Question

Find the mean from the following table: 

Hint:

Always find the midpoint for each class interval and use \( \bar{x} = \dfrac{\sum fx}{\sum f} \) to calculate the mean for grouped data.

Answer 1

Step 1: Find the midpoints (x).
\[ x = 5, 15, 25, 35, 45 \]
Step 2: Multiply each frequency by midpoint.
\[ \sum f = 3 + 10 + 11 + 9 + 7 = 40 \] \[ \sum fx = (3)(5) + (10)(15) + (11)(25) + (9)(35) + (7)(45) \] \[ \sum fx = 15 + 150 + 275 + 315 + 315 = 1070 \]
Step 3: Find the mean.
\[ \bar{x} = \frac{\sum fx}{\sum f} = \frac{1070}{40} = 26.75 \]
Step 4: Final Answer.
\[ \boxed{\text{Mean} = 26.75} \]