Question

Find the mode from the following table: 

Hint:

The modal class is the class interval with the highest frequency. Always apply the mode formula using $f_1, f_0, f_2$ correctly.

Answer 1

Step 1: Identify the modal class. 
The class with the highest frequency is \(30–40\), so it is the modal class. 
Step 2: Write the given data. 
\[ L = 30, \quad f_1 = 23, \quad f_0 = 21, \quad f_2 = 14, \quad h = 10 \] Step 3: Apply the formula for mode. 
\[ \text{Mode} = L + \left(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h \] Step 4: Substitute the values. 
\[ \text{Mode} = 30 + \left(\dfrac{23 - 21}{2(23) - 21 - 14}\right) \times 10 \] \[ = 30 + \left(\dfrac{2}{46 - 35}\right) \times 10 = 30 + \dfrac{20}{11} = 31.82 \] Step 5: Conclusion. 
Hence, the mode = 31.82 (approx.).