1. **Stating the problem:** We need to find the measures of central tendency (mean, median, mode) for grouped data using their respective formulas. 2. **Mean formula for grouped data:** $$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$ where $f_i$ is the frequency of the $i^{th}$ class and $x_i$ is the midpoint of the $i^{th}$ class. 3. **Median formula for grouped data:** $$\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f_m}\right) \times h$$ where: - $L$ = lower boundary of median class - $N$ = total frequency - $F$ = cumulative frequency before median class - $f_m$ = frequency of median class - $h$ = class width 4. **Mode formula for grouped data:** $$\text{Mode} = L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$$ where: - $L$ = lower boundary of modal class - $f_1$ = frequency of modal class - $f_0$ = frequency of class before modal class - $f_2$ = frequency of class after modal class - $h$ = class width 5. **Explanation:** - Calculate midpoints $x_i$ for each class. - Multiply each midpoint by its frequency and sum to find numerator for mean. - Sum all frequencies for denominator. - Find median class where cumulative frequency crosses $N/2$. - Use median formula with values from frequency table. - Identify modal class with highest frequency. - Use mode formula with frequencies of modal and adjacent classes. 6. **Intermediate work:** - Show midpoint calculations. - Show cumulative frequencies. - Show substitution into formulas. This approach allows calculating mean, median, and mode for grouped data accurately using their formulas.