The following table shows the age distribution of patients admitted during a day in two different hospitals : | Age (in years) : | 5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | |---|---|---|---|---|---|---| | Number of Patients admitted in Hospital I : | 6 | 11 | 21 | 23 | 14 | 5 | | Number of Patients admitted in Hospital II : | 8 | 16 | 32 | 10 | 24 | 12 | Based on the above information, answer the following questions : (i) In Hospital I, what is the upper limit of modal class. (1) (ii) In Hospital II, what is the lower limit of modal class. (1) (iii) (a) Find the mode of the data of Hospital I. (2) OR (b) Find the mode of the data of Hospital II. (2)

Step 1: Identify Modal Class for Hospital I

To find the modal class for Hospital I, we need to identify the class interval with the highest frequency. Looking at the 'Number of Patients admitted in Hospital I' row, the highest frequency is 23, which corresponds to the age group 35 - 45 years.

Step 2: Determine Upper Limit of Modal Class for Hospital I

The modal class for Hospital I is 35 - 45. The upper limit of this class interval is 45.

Step 3: Identify Modal Class for Hospital II

Similarly, for Hospital II, we find the class interval with the highest frequency. The highest frequency in the 'Number of Patients admitted in Hospital II' row is 32, which corresponds to the age group 25 - 35 years.

Step 4: Determine Lower Limit of Modal Class for Hospital II

The modal class for Hospital II is 25 - 35. The lower limit of this class interval is 25.

Step 5: Calculate Mode for Hospital I

For Hospital I, the modal class is 35 - 45. Here, $L = 35$ (lower limit), $f_1 = 23$ (frequency of modal class), $f_0 = 21$ (frequency of preceding class), $f_2 = 14$ (frequency of succeeding class), and $h = 10$ (class size). We substitute these values into the mode formula for grouped data.

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