Draw a cumulative frequency curve (ogive) for the following distribution
`{:(" Mark ", 5 -10,10-15,15-20,20-25,25-30),(" no. of students "," "7, " "9, " "12, " "8, " "6):}`

Answer

To draw a cumulative frequency curve (ogive) for the given distribution, we will follow these steps:

### Step 1: Create a Cumulative Frequency Table
We need to calculate the cumulative frequencies for the given data.

| Mark Range | No. of Students | Cumulative Frequency |
|------------|-----------------|----------------------|
| 5 - 10 | 7 | 7 |
| 10 - 15 | 9 | 7 + 9 = 16 |
| 15 - 20 | 12 | 16 + 12 = 28 |
| 20 - 25 | 8 | 28 + 8 = 36 |
| 25 - 30 | 6 | 36 + 6 = 42 |

### Step 2: Determine the Class Boundaries for the Ogive
For the less than type ogive, we will use the upper boundaries of the class intervals.

- Less than 10
- Less than 15
- Less than 20
- Less than 25
- Less than 30

### Step 3: Prepare the Data for Plotting
Now, we will prepare the data points for plotting:

| Less Than (x) | Cumulative Frequency (y) |
|----------------|--------------------------|
| 10 | 7 |
| 15 | 16 |
| 20 | 28 |
| 25 | 36 |
| 30 | 42 |

### Step 4: Draw the Axes
On a graph paper, draw two perpendicular lines to represent the x-axis and y-axis. Label the x-axis as "Less Than Marks" and the y-axis as "Cumulative Frequency".

### Step 5: Set the Scale
Choose an appropriate scale for both axes. For example:
- On the x-axis, let 1 unit = 5 marks.
- On the y-axis, let 1 unit = 5 students.

### Step 6: Plot the Points
Using the table from Step 3, plot the points on the graph:
- (10, 7)
- (15, 16)
- (20, 28)
- (25, 36)
- (30, 42)

### Step 7: Draw the Ogive
Connect the points with a smooth curve. Start from the point (10, 7) and draw a freehand curve through the other points to form the ogive.

### Step 8: Label the Ogive
Finally, label the ogive as "Cumulative Frequency Curve" or "Ogive".