find mode class interval - 0-10 10-20 20-30 30-40 40-50 50-60 frequency - 4 6 7 12 5 6
Given the class intervals and frequencies:
- Class Intervals: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
- Frequencies: 4, 6, 7, 12, 5, 6
Step 1: Identify the modal class
The modal class is the class with the highest frequency. Here, the highest frequency is 12, which corresponds to the class interval 30-40.
Step 2: Apply the mode formula
{Mode} = L + ( {f_1 - f_0} ÷ {2f_1 - f_0 - f_2}) × h
Where:
- \( L = 30 \) (lower boundary of the modal class)
- \( f_1 = 12 \) (frequency of the modal class)
- \( f_0 = 7 \) (frequency of the class preceding the modal class)
- \( f_2 = 5 \) (frequency of the class succeeding the modal class)
- \( h = 10 \) (class width)
Step 3: Substitute the values into the formula
{Mode} = 30 + \left( \frac{12 - 7}{2(12) - 7 - 5} \right) \times 10
{Mode} = 30 + \left( \frac{5}{24 - 12} \right) \times 10
{Mode} = 30 + \left( \frac{5}{10} \right) \times 10
{Mode} = 30 + \left( 0.5 \times 10 \right)
{Mode} = 30 + 5
Final Answer:
{Mode} = 35
So, the mode of the given data is 35
