Less than type of cumulative frequency distribution:

To convert the given distribution into a less than type of cumulative frequency distribution, we need to calculate the cumulative frequency for each class interval. The cumulative frequency for a class interval is the sum of the frequencies of that class interval and all the previous class intervals.

To calculate the cumulative frequency, we can start with the first class interval and add the frequency of that interval to get the cumulative frequency for that interval. Then, we add the cumulative frequency of the first interval to the frequency of the second interval to get the cumulative frequency for the second interval, and so on.

Class Interval No. of workers Cumulative Frequency
400-420 12 12
420-440 14 26
440-460 8 34
460-480 6 40
480-500 10 50

Ogive:

To draw the ogive, we plot the cumulative frequency on the y-axis and the upper class limit of each interval on the x-axis. We then join the points on the graph with straight lines.

To plot the ogive, we can use the cumulative frequency and the upper class limit for each interval.

Upper Class Limit Cumulative Frequency
420 12
440 26
460 34
480 40
500 50

Now, we can plot these points on a graph and join them with straight lines to obtain the ogive.

Explanation:

The less than type of cumulative frequency distribution shows the cumulative frequency for each class interval, which represents the number of observations that are less than or equal to the upper class limit of that interval.

The ogive is a graphical representation of the cumulative frequency distribution. It helps us visualize the cumulative frequency distribution and understand the distribution of data.

In this case, the given distribution represents the daily income of 50 workers in a factory. By converting it to a less than type of cumulative frequency distribution, we can see how many workers earn less than or equal to a certain income level.

The ogive helps us understand the distribution of income among the workers and identify the income levels at which a certain percentage of workers fall below. It is a useful tool for analyzing and interpreting data.