NCERT Solutions for Class 10 Maths Exercise 14.4 Statistics

Contents are updated according to new CBSE Curriculum and based on updated NCERT Books issued for all boards. All the PDF solutions are available in Hindi and English medium along with the videos, so UP Board and MP board students also take the benefits of these solutions.

Graphical Representation of Cumulative Frequency Distribution

We have already studied; Pictures speak better than words. A graphical representation helps us understand the data given at a glance. In earlier classes, we have represented data through bar graphs, histograms, and frequency polygons. In class 10, we will learn to represent the cumulative frequency distribution graphically.

How to draw an Ogive?

To graph the data in the table, we mark the upper bounds of the square intervals on the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis (y-axis), selecting an appropriate scale. The scale on both axes may not be the same. Let us now plot the points corresponding to the orders given by the given pairs (upper limit, corresponding cumulative frequency) on a graph paper, and join them through a smooth freehand curve. The curve we obtain is called the cumulative frequency curve or warhead (less than type).

What is an Ogive?

The word “Ogive” is pronounced as “ojeev” and is derived from the word ogee. An ogee is a figure consisting of a concave arch that flows into a convex arch, forming an S-shaped curve with vertical ends. Architecturally, the OG shape is one of the characteristics of fourteenth and fifteenth century Gothic styles.

How to find Median from Ogive?

Draw both ogives (i.e. less than type and more than type) on the same axis. Two ogives will intersect at one point. From this point, if we draw a perpendicular line on the x-axis, the point where it crosses the x-axis gives us the median.
To calculate the mode and median for the grouped data, you must ensure that the square interval is constant before applying the formulas. The same situation applies to the construction of a warhead. Also, in the case of warheads, the scale on both axes may not be the same.