An ogive, also known as a cumulative frequency curve, is a graphical representation used in statistics to show the cumulative frequency distribution of a dataset.

It helps visualize how many data points fall below or equal to a certain value. Constructing an ogive involves the following steps:

**Data Preparation**: Begin with a dataset containing raw data values.**Data Sorting**: Arrange the data in ascending order from smallest to largest.**Frequency Table**: Create a frequency table that lists the data values, their frequencies (how often they occur), and cumulative frequencies (the running total of frequencies).**Cumulative Frequency Calculation**: Calculate the cumulative frequency by adding up the frequencies from the lowest data value to the highest.**Plotting the Ogive**: Now, you can create a graph with the x-axis representing data values and the y-axis representing cumulative frequencies. You can choose to use a line graph or a step graph (with horizontal lines connecting the cumulative frequencies at each data point).

Let’s illustrate this process with an example:

Suppose you have the following dataset representing the ages of a group of people:

`25, 28, 30, 32, 35, 36, 38, 40, 42, 45`

**Data Sorting**:

Sort the data in ascending order:

` 25, 28, 30, 32, 35, 36, 38, 40, 42, 45`

**Frequency Table**:

Create a frequency table with columns for data values, frequencies, and cumulative frequencies:

```
| Data Value | Frequency | Cumulative Frequency |
|------------|-----------|----------------------|
| 25 | 1 | 1 |
| 28 | 1 | 2 |
| 30 | 1 | 3 |
| 32 | 1 | 4 |
| 35 | 1 | 5 |
| 36 | 1 | 6 |
| 38 | 1 | 7 |
| 40 | 1 | 8 |
| 42 | 1 | 9 |
| 45 | 1 | 10 |
```

**Plotting the Ogive**:

Now, plot the ogive using the data values on the x-axis and the cumulative frequencies on the y-axis. You can connect the points with lines to create the ogive curve. The resulting ogive will show how the data is distributed in terms of cumulative frequencies, helping you visualize, for example, how many people are aged 38 or younger (cumulative frequency of 7) or 40 or younger (cumulative frequency of 8).

This graphical representation is helpful for understanding the distribution of data and finding percentiles or quartiles within the dataset.