Question

The following table gives the height of trees.

Height	Less than \[7\]	Less than \[14\]	Less than \[21\]	Less than \[28\]	Less than \[35\]	Less than \[42\]	Less than \[49\]	Less than\[56\]
No of trees	\[25\]	\[45\]	\[95\]	\[140\]	\[235\]	\[275\]	\[320\]	\[360\]

Draw “less than” ogive and “more than” ogive.

Answer 1

Hint: From the given question we are asked to draw a “less than type” graph and “more than” ogive graph for the above data regarding height and number of trees. For finding the graph we will take the help of statistics and find the table for cumulative frequency. After finding the cumulative frequency to the number of students' tables we will plot the graph.

Complete step by step answer:
Now, we prepare the cumulative frequency table for less than series.
Here for height class the lower and upper boundary will be the height of the previous class and that present class respectively.
Cumulative frequency will be the sum of the total number of trees of previous and that present class.
For suitable points the x-coordinate is that class upper boundary and the y-coordinate will be the cumulative frequency of that class.

Height(less than)	Heightclass	Number oftrees	Cumulative frequency	Suitable points
\[7\]	\[0-7\]	\[26\]	\[26\]	\[(7,26)\]
\[14\]	\[7-14\]	\[31\]	\[57\]	\[(14,57)\]
\[21\]	\[14-21\]	\[35\]	\[92\]	\[(21,92)\]
\[28\]	\[21-28\]	\[42\]	\[134\]	\[(28,134)\]
\[35\]	\[28-35\]	\[82\]	\[216\]	\[(35,216)\]
\[42\]	\[35-42\]	\[71\]	\[287\]	\[(42,287)\]
\[49\]	\[42-49\]	\[54\]	\[341\]	\[(49,314)\]
\[56\]	\[49-56\]	\[19\]	\[360\]	\[(56,360)\]

Now we will draw the less than ogive curve using the suitable points which are in the above table.

Here the x-axis will be the number of trees and y-axis will be cumulative frequency.
Now, we prepare the cumulative frequency table for more than series in the same way but the cumulative frequency will be inverse order.

Height(more than)	Heightclass	Number ofTrees	Cumulative frequency	Suitable points
\[7\]	\[0-7\]	\[26\]	\[360\]	\[(0,360)\]
\[14\]	\[7-14\]	\[31\]	\[334\]	\[(7,334)\]
\[21\]	\[14-21\]	\[35\]	\[303\]	\[(14,303)\]
\[28\]	\[21-28\]	\[42\]	\[268\]	\[(21,268)\]
\[35\]	\[28-35\]	\[82\]	\[226\]	\[(28,226)\]
\[42\]	\[35-42\]	\[71\]	\[144\]	\[(35,144)\]
\[49\]	\[42-49\]	\[54\]	\[73\]	\[(42,73)\]
\[56\]	\[49-56\]	\[19\]	\[54\]	\[(49,54)\]

Now we will use the suitable points in the above cumulative frequency table for more than series and we will draw the required graph.
where the x-axis will be the number of trees and y-axis will be cumulative frequency.

Note: Students must be very careful in plotting the points. We should take a perfect scale in the graph so that the graph does not become difficult to understand or not become big one. So, we must take the unit in the x-axis as \[10\] and the y axis as \[50\]. Students should know that cumulative frequency is different for less than and more than curves. The Ogive curve is defined as a frequency distribution graph of a series.