Draw the histogram for the following
`{:("Class mark ", 25,35,45,55,65),(" Frequency ",7,15,18,12,8):}`

Answer

To draw a histogram for the given class marks and frequencies, follow these steps:

### Step-by-Step Solution:

1. **Identify Class Marks and Frequencies**:
- Class Marks: 25, 35, 45, 55, 65
- Frequencies: 7, 15, 18, 12, 8

2. **Determine Class Intervals**:
- Since class marks are given, we can assume that each class mark represents the midpoint of a class interval.
- We can define the class intervals as follows:
- For 25: Class Interval = [20, 30]
- For 35: Class Interval = [30, 40]
- For 45: Class Interval = [40, 50]
- For 55: Class Interval = [50, 60]
- For 65: Class Interval = [60, 70]

3. **Set Up the Axes**:
- Draw the horizontal axis (x-axis) for class intervals and the vertical axis (y-axis) for frequencies.
- Label the x-axis with the class intervals: 20-30, 30-40, 40-50, 50-60, 60-70.
- Label the y-axis with frequencies, ensuring to cover the maximum frequency (18 in this case).

4. **Choose a Scale**:
- Decide on a scale for the axes. For example:
- 1 unit on the y-axis = 2 frequency units
- 1 unit on the x-axis = 10 units (for class intervals)

5. **Plot the Frequencies**:
- For each class interval, plot the frequency:
- For the interval [20, 30], the frequency is 7. Draw a bar from 20 to 30 reaching up to 7 on the y-axis.
- For the interval [30, 40], the frequency is 15. Draw a bar from 30 to 40 reaching up to 15 on the y-axis.
- For the interval [40, 50], the frequency is 18. Draw a bar from 40 to 50 reaching up to 18 on the y-axis.
- For the interval [50, 60], the frequency is 12. Draw a bar from 50 to 60 reaching up to 12 on the y-axis.
- For the interval [60, 70], the frequency is 8. Draw a bar from 60 to 70 reaching up to 8 on the y-axis.

6. **Draw the Bars**:
- Ensure that the bars are of equal width and are adjacent to each other without any gaps.
- The height of each bar corresponds to the frequency of the respective class interval.

7. **Label the Histogram**:
- Add titles and labels to the histogram for clarity. Title the graph "Histogram of Class Marks and Frequencies".
- Label the x-axis as "Class Intervals" and the y-axis as "Frequency".

### Final Histogram:
- You should now have a completed histogram representing the frequencies of the respective class intervals based on the given class marks.