The image contains a question asking for the calculation of the median and modal class from a frequency distribution table. Let’s break down the table and question.

Frequency Distribution Table

Total consumers (N) = 50.

Questions from the image:

1. Formula to calculate the median of a continuous series: $M_d = L + \left( \frac{\frac{N}{2} - c.f.}{f} \right) \times h$ Where:

   • $L$ = lower boundary of the median class,
   • $N$ = total frequency,
   • $c.f.$ = cumulative frequency before the median class,
   • $f$ = frequency of the median class,
   • $h$ = class width.

2. Finding the modal class and median class:

   • The modal class is the class with the highest frequency, which is 70-80 (with frequency 15).
   • The median class is calculated by finding $\frac{N}{2}$. In this case, $\frac{50}{2} = 25$, so the class where the cumulative frequency first exceeds 25 is the median class, which is also 70-80.

3. Calculating the median: Median class = 70-80:

   • $L = 70$,
   • $N = 50$,
   • $c.f. = 14$ (cumulative frequency before the median class),
   • $f = 15$,
   • $h = 10$ (class width).

   Using the formula: $M_d = 70 + \left( \frac{25 - 14}{15} \right) \times 10$ Simplifying: $M_d = 70 + \left( \frac{11}{15} \right) \times 10 = 70 + 7.33 = 77.33$ Therefore, the median is 77.33 units.

4. Are the modal and median classes always the same?

   • No, not always. In this case, they are the same, but the modal class is determined by the highest frequency, while the median class is based on the cumulative frequency reaching half the total. They can be different depending on the distribution.

Let me know if you want further details or have any questions! Here are five related questions:

1. What happens when the modal class is different from the median class?
2. How do you interpret a continuous series in statistics?
3. What is the difference between mode and median in terms of data interpretation?
4. Can a dataset have more than one mode?
5. What is the impact of class width on the calculation of the median?

Tip: Always make sure to calculate cumulative frequencies accurately when finding the median in a continuous frequency distribution.