Question

Find the mode of the following frequency table : 

Hint:

The Mode should always lie within the modal class (30-40). If your answer is outside this range, re-check your calculations.

Answer 1

Step 1: Understanding the Concept:
The Mode of a grouped frequency distribution is the value within the modal class (the class with the highest frequency) calculated using a specific formula.
Step 2: Identifying Modal Class and Values:
The maximum frequency is 15, so the modal class is 30-40.
$l$ (lower limit) = 30
$f_1$ (frequency of modal class) = 15
$f_0$ (frequency of preceding class) = 10
$f_2$ (frequency of succeeding class) = 11
$h$ (class size) = 10
Step 3: Applying the Formula:
Mode $= l + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h$ \[ \text{Mode} = 30 + \left[ \frac{15 - 10}{2(15) - 10 - 11} \right] \times 10 \] \[ \text{Mode} = 30 + \left[ \frac{5}{30 - 21} \right] \times 10 = 30 + \frac{50}{9} \] \[ \text{Mode} = 30 + 5.55... = 35.56 \text{ approx} \]
Step 4: Final Answer:
The mode of the frequency table is 35.56.