1. **Problem Statement:** Find the mode of the grouped data given the class intervals and their frequencies. 2. **Data:** Class intervals (No of visit): 5-9, 10-14, 15-19, 20-24, 25-29, 30-34 Frequencies: 6, 11, 18, 25, 20, 10 3. **Formula for Mode in 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 4. **Step 1: Identify the modal class** The modal class is the class with the highest frequency. Frequencies: 6, 11, 18, 25, 20, 10 Highest frequency = 25 corresponding to class 20-24. So, modal class = 20-24 5. **Step 2: Determine values for formula** - $L = 20$ (lower boundary of modal class) - $f_1 = 25$ (frequency of modal class) - $f_0 = 18$ (frequency of class before modal class, 15-19) - $f_2 = 20$ (frequency of class after modal class, 25-29) - $h = 5$ (class width, difference between lower limits 20 - 15 = 5) 6. **Step 3: Calculate mode** $$\text{Mode} = 20 + \left(\frac{25 - 18}{2 \times 25 - 18 - 20}\right) \times 5$$ $$= 20 + \left(\frac{7}{50 - 38}\right) \times 5$$ $$= 20 + \left(\frac{7}{12}\right) \times 5$$ $$= 20 + 2.9167 = 22.9167$$ 7. **Interpretation:** The mode of the data is approximately 22.92. This means the most frequent number of visits falls around 23 visits in the given grouped data. This value represents the visit count interval where the highest concentration of data points lies.