1. **Problem Statement:** Find the mean, mode, and median of the frequency distribution with frequencies: 4, 4, 7, 10, 12, 8, 5. 2. **Step 1: Organize the data** Since only frequencies are given, assume the class marks or values as $x_1, x_2, \ldots, x_7$. Without explicit class values, we treat frequencies as data points for mean, mode, and median calculation. 3. **Step 2: Calculate the Mean** The mean formula for frequency distribution is: $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$ Here, since values are not given, assume values as $1, 2, 3, 4, 5, 6, 7$ corresponding to frequencies. Calculate total frequency: $$N = 4 + 4 + 7 + 10 + 12 + 8 + 5 = 50$$ Calculate $\sum f_i x_i$: $$= 4\times1 + 4\times2 + 7\times3 + 10\times4 + 12\times5 + 8\times6 + 5\times7$$ $$= 4 + 8 + 21 + 40 + 60 + 48 + 35 = 216$$ Therefore, $$\text{Mean} = \frac{216}{50} = 4.32$$ 4. **Step 3: Calculate the Mode** Mode is the value with the highest frequency. Highest frequency = 12 (at value 5) So, Mode = 5 5. **Step 4: Calculate the Median** Median is the middle value when data is arranged in order. Total frequency $N=50$, median position = $\frac{N}{2} = 25$th value. Cumulative frequencies: - Up to 1: 4 - Up to 2: 4 + 4 = 8 - Up to 3: 8 + 7 = 15 - Up to 4: 15 + 10 = 25 The 25th value lies in the class with value 4. So, Median = 4 **Final answers:** - Mean = 4.32 - Mode = 5 - Median = 4