**Calculating Mean, Median and Mode of Continuous Series**

To calculate the mean, median, and mode of a continuous series, follow the steps outlined below:

**Step 1: Understand the Data**

Before calculating the mean, median, and mode, it is important to understand the data and its characteristics. A continuous series refers to a set of data that can take any value within a given range. For example, the heights of individuals can be considered as a continuous series.

**Step 2: Group the Data**

To simplify the calculation process, it is often helpful to group the data into intervals or classes. These intervals should cover the entire range of the data and have equal width. For example, if the data ranges from 150 cm to 190 cm, the intervals could be set at 150-160 cm, 160-170 cm, etc.

**Step 3: Determine the Midpoints**

For each interval, determine the midpoint by taking the average of the upper and lower limits. For example, if the interval is 150-160 cm, the midpoint would be (150 + 160) / 2 = 155 cm.

**Step 4: Calculate the Frequency**

Count the number of observations falling within each interval. This is known as the frequency. For example, if there are 10 individuals with heights between 150-160 cm, the frequency for that interval would be 10.

**Step 5: Calculate the Mean**

The mean of a continuous series can be calculated using the formula:

Mean = (Sum of (Midpoints × Frequencies)) / Total Frequency

Multiply each midpoint by its corresponding frequency, sum up these products, and divide by the total frequency to find the mean.

**Step 6: Calculate the Median**

To find the median of a continuous series, follow these steps:

1. Determine the cumulative frequency, which is the running total of the frequencies.
2. Find the median class, which is the class that contains the median value. This is typically the class with the cumulative frequency closest to half of the total frequency.
3. Use the following formula to calculate the median:

Median = Lower Limit of Median Class + [(Total Frequency / 2) - Cumulative Frequency of Previous Class] × Interval Width / Frequency of Median Class

The lower limit of the median class is the lowest value within that class. The interval width is the difference between the upper and lower limits of the class.

**Step 7: Calculate the Mode**

The mode of a continuous series is the value or class that occurs most frequently. To calculate the mode, identify the class with the highest frequency. If there are multiple classes with the same highest frequency, they are all considered modes.

**Step 8: Present the Results**

After calculating the mean, median, and mode, present the results in a clear and organized manner. It is common to include a table displaying the intervals, midpoints, frequencies, and cumulative frequencies.

By following these steps, you can accurately calculate the mean, median, and mode of a continuous series. Remember to ensure that the data is properly grouped into intervals and that all calculations are carried out accurately.