Question

What is the lower limit of the median class ?

Answer 1

The cumulative frequency is calculated as follows: \[ \begin{array}{|c|c|c|} \hline \textbf{Class} & \textbf{Frequency (f)} & \textbf{Cumulative Frequency} \\ \hline 20 - 25 & 5 & 5 \\ 25 - 30 & 15 & 20 \\ 30 - 35 & 25 & 45 \\ 35 - 40 & 30 & 75 \\ 40 - 45 & 15 & 90 \\ 45 - 50 & 10 & 100 \\ \hline \end{array} \] Since $n/2 = 100/2 = 50$, the median class is $35 - 40$. Correct Answer: The lower limit of the median class is $35$.

Answer 2

The modal class corresponds to the highest frequency, which is $30$ for the class $35 - 40$.
The upper limit of the modal class is:
Correct Answer: $40$.

Answer 3

\[ \text{Median} = l + \left( \frac{\frac{n}{2} - CF}{f_m} \right) \times h, \] where: $l = 35$ (lower limit of the median class),  $n = 100$ (total frequency),  $CF = 45$ (cumulative frequency of the class before the median class),  $f_m = 30$ (frequency of the median class),  $h = 5$ (class width).  Substituting: \[ \text{Median} = 35 + \left( \frac{50 - 45}{30} \right) \times 5 = 35 + \left( \frac{5}{30} \right) \times 5 = 35 + \frac{25}{30} = 35.83. \] Correct Answer: Median = 35.83. 

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Modal Class Calculation:  The modal class is identified as the class with the highest frequency. From the table, the highest frequency is 30, which corresponds to the class $35 - 40$. Correct Answer: Modal class is $35 - 40$.