Question

Construct class intervals and frequencies for the following distribution table. Also draw the ogive curves for the same.

Marks obtained Less than 5 Less than 10 Less than 15 Less than 20 Less than 25
No of students 2 8 18 27 35

Answer 1

To construct class intervals and frequencies for a distribution table, you need to identify the range of the data, determine the width and length of each interval, count the number of observations falling in each interval, and plot them on a histogram and give a curve.

Step-by-step explanation:

Constructing Class Intervals and Frequencies for a Distribution Table

To construct class intervals and frequencies for the given distribution table:

1. Identify the range of marks obtained, which is from 0 to 35.
2. Determine the width of each class interval by dividing the range by the desired number of intervals (e.g. 5 or 6). For this example, let's choose 6 intervals.
3. Calculate the length of each interval by dividing the range by the number of intervals, rounding up if necessary. In this case, the length is 6.
4. Start with the lower bound of the first interval, which is 0, and add the length to find the upper bound. Repeat this process until you have determined the upper bounds for all intervals. For example, the first interval is 0-6, the second interval is 6-12, and so on.
5. Count the number of students falling within each interval and record it as the frequency.
6. Once you have the class intervals and frequencies, you can construct the histogram by plotting the class intervals on the x-axis and the frequencies on the y-axis. Use a ruler and pencil to sketch the graph and scale the axes accordingly.
7. To draw the ogive curve, plot the cumulative frequency on the y-axis and the upper bounds of the class intervals on the x-axis. Connect the points with smooth curves.

By following these steps, you can construct the required class intervals, and frequencies, draw the histogram and ogive curves for the given distribution table.