Jay Deshabandu

Director,

Department of Mathematics

Faculty of Science and Technology

National Institute of Education

Maharagma

I became interested in giving a Mathematics contest in order to increase and motivate our students’ interest in learning Mathematics. In order to design a Mathematics test, I read your grade 11 Mathematics syllabus which is officially published by your institute.

In the Statistics part of the syllabus, the definition of a histogram is not what the rest of the world follows. In your syllabus it says that a digram of frequencies verses class widths as a histogram. And, it further clearly indicates that in the case of equal class widths, the area of a bar is equal to the frequency.  In a formal definition of many good books on Statistics, The y-axis is chosen as frequency density-not just frequency. Thus frequency density times the class width gives the area of the bars which is the frequency. Please note that If frequencies are chosen for y-axis, it is called a bar graph not a histogram.

The proper definition is a key to begin a study of probability distributions because in a discrete probability distribution, the y-axis is chosen for the probability density function, which is equal to a histogram where y-axis is chosen as relative frequency density. So the proper definition lends to the idea of probability density function for a discrete random variable.  The idea of a probability density function for a continuous function is an extension of the idea of probability distribution function for a discrete random variable.

Besides, if our students use the definition of a histogram according to your syllabus, they will give wrong answers to international examinations in Statistics such as A-level, Cambridge International Examinations and M.E. I and Edexcel.

I hope that you would pay your kind attention to the above for the sake of Students in Sri Lanka.