Question

Find the mode of the following frequency table: 

Hint:

In frequency distributions, mode lies near the class with the highest frequency. Use the formula carefully with correct \(f_0, f_1, f_2\).

Answer 1

Step 1: Identify the modal class.
The class with the highest frequency is \(60–80\) (frequency \(= 12\)). Hence, the modal class is \(60–80\).
Step 2: Recall the formula for mode.
\[ \text{Mode} = L + \frac{(f_1 - f_0)}{2f_1 - f_0 - f_2} \times h \] where \(L =\) lower limit of modal class, \(f_1 =\) frequency of modal class, \(f_0 =\) frequency of class preceding modal class, \(f_2 =\) frequency of class succeeding modal class, and \(h =\) class width.
Step 3: Substitute the values.
\[ L = 60, \; f_1 = 12, \; f_0 = 10, \; f_2 = 6, \; h = 20 \]
Step 4: Apply the formula.
\[ \text{Mode} = 60 + \frac{(12 - 10)}{2(12) - 10 - 6} \times 20 \] \[ = 60 + \frac{2}{24 - 16} \times 20 = 60 + \frac{2}{8} \times 20 = 60 + 5 = 65 \]
Step 5: Conclusion.
Hence, the mode of the distribution is \(\boxed{65}\).