Let's solve the questions using the information in the table.

Given Information

The table shows time spent exercising in intervals and the corresponding frequencies:

• $0 < x \leq 10$: Frequency = 18
• $10 < x \leq 20$: Frequency = 14
• $20 < x \leq 30$: Frequency = 3
• $30 < x \leq 40$: Frequency = 16
• $40 < x \leq 50$: Frequency = 21
• $50 < x \leq 60$: Frequency = 7

a) Modal Class

The modal class is the interval with the highest frequency. From the table, we can see that the interval $40 < x \leq 50$ has the highest frequency of 21.

Answer: The modal class is $40 < x \leq 50$.

b) Median Class

To find the median class, we need to determine the class interval that contains the median value.

1. Total frequency = $18 + 14 + 3 + 16 + 21 + 7 = 79$.

2. The median position in a frequency distribution is given by $\frac{n+1}{2}$, where $n$ is the total frequency. So, the median position is: $\frac{79 + 1}{2} = 40$

3. Now, we need to locate this median position within the cumulative frequency:

   • Cumulative frequency up to $0 < x \leq 10$ = 18
   • Cumulative frequency up to $10 < x \leq 20$ = 18 + 14 = 32
   • Cumulative frequency up to $20 < x \leq 30$ = 32 + 3 = 35
   • Cumulative frequency up to $30 < x \leq 40$ = 35 + 16 = 51

   The median falls within the interval $30 < x \leq 40$ since the 40th value is within the cumulative frequency of 51.

Answer: The median class is $30 < x \leq 40$.

Would you like more details or have any questions on these answers?

Here are 5 related questions that expand on this information:

1. How do you find the mean value of the time spent exercising using the data in the table?
2. What is the significance of the median in understanding the data distribution?
3. Can you calculate the range of time spent exercising using the given intervals?
4. How would you determine the lower quartile (Q1) from this grouped data?
5. What is the difference between a modal class and the mean of a data set?

Tip: When analyzing grouped data, always check the cumulative frequency to quickly locate measures like the median and quartiles.