## Ishu got 80% mark in CBSE

Ms Rania Ali has a unique way of teaching. Often, she does this through stories which relate to their interests. Here is one of her stories.

Ms Rania Ali: I am sure your parents have asked you to work hard, focus on your studies so that you can do well in your exams. You know that they love you and want you to be able to get into good colleges for subjects of your choices.

This story is about one Mr Rahul Verma who kept telling his daughter Ishu to study hard. Well, Ishu was a good student when she wrote her grade 12 CBSE exam. (CBSE is central board of secondary education and the exam is written all over India by over 100,000 students).

Ishu: Dad, in my CBSE exam, I got 80% marks which is 10% more than the 70% you got in your secondary school exam.

Dad: Ishu, the grades these days are inflated compared to my days.

Ishu: Dad, just admit it. I did better than you did.

Dad: Not so fast. There is a way of checking this out. Your mark was higher than how many percent of the students who wrote the exam this year?

## Percentile Ranking

Ishu: You mean my percentile ranking ? We can check that at the website https://varic.com/percentile/xv.

They went to the website and calculated the percentile marks for different percentages.

2015 CBSE Grade 12 | ||

% Mark | Percentile Ranking | Interval and % Frequency |

100 | 100 | |

90 | 89 | 90-100 (11) |

80 | 69 | 80-90 (20) |

70 | 46 | 70-80 (23) |

60 | 25 | 60-70 (21) |

50 | 12 | 50-60 (11) |

40 | 4 | 40-50 (8) |

30 | 1 | 30-40 (3) |

20 | 0.1 | 20-30 (0.9) |

Ishu: See dad. I had 80% marks which were at a percentile of 69 which means I had better marks than 69% of all the students. I also calculated that 71.8% mark was better than 50% of the students.

Dad: I have a record of the percent marks to percentile mark from my year. Here it is. The mark of 80% in that year would have a percentile of 99.8 rather than 70 in your year. My mark of 70% in that year had a percentile of 90. So your mark was better than 70% of all the students. This is good but mine was much more competitive. It was better than 90% of all the students. The 50 percentile was for a mark of 40%.

1962 Senior Secondary | ||

% Mark | Percentile Ranking | Interval and % Frequency |

90 | 100 | 90-100 (0) |

80 | 99.8 | 80-90 (0.2) |

70 | 95 | 70-80 (4.8) |

60 | 90 | 60-70 (5) |

50 | 70 | 50-60(20) |

40 | 45 | 40-50 (25) |

30 | 25 | 30-40 (20) |

20 | 15 | 20-30 (10) |

10 | 5 | 10-20 (10) |

0 | 0 | 0-10 (5) |

Ramu (one of the students) raised his hand and asked for further explanation for why the marks in the two years were so different.

Ms. Rania Ali: There are two factors. One is that in the year of the dad, the answers had to be descriptive. It was harder to judge what a perfect answer would be and most of the time the maximum mark was not given except in subjects like maths. In Ishu’s year, there were multiple choice questions. Each answer would be either correct for full marks or wrong for no mark. The second reason is the grade inflation because there is a tendency now to exclude really tough questions from the exams.

Another student named Ritu: Madam, it was convincing that Dad was right and not Ishu. Are there any other applications of percentiles ?

Ms. Rania Ali: Ritu, I like your sense of humor. There are many applications of percentiles. Let us start with your college admission. Colleges use percentiles to determine the order of admission of the students whether it is the CBSE scores, their own admission tests or tests such as SAT and MCAT. Doctors use it to determine the health of babies. Speed limits on roads are set as 85 percentile of the speed at which cars drive on them.

**Central tendencies **

Ms Rania Ali continued. I have a graph of your marks from the last test. Let us ask the question, where is the centre of this graph.

Ritu: Somewhere in the middle where the average mark is. We can add all the marks and divide them by the number of students. This will give us the average mark.

Ms. Rania Ali: Ritu, good thinking. This is called the mean mark. I calculated it to be 70.

Ramu: Why can’t we use the percentile thing ? 50 percentile mark would be more than that of half the class. I can see on the chart that it is 74%. No need to add marks and divide.

Ms. Rania Ali: Ramu, 50 percentile is also called the median. So the median mark is 74.

Sonia: I am into fashion and I like what is most popular. Can we just go with that? The most common mark on the graph is 76. I see that five students got this mark.

Ms. Rania Ali: Sonia, you have brought us to the idea of mode. The most frequent mark is called the mode.

Ramu: I see a problem. Mean, median and mode are all different.

Sonia: Ramu, they are all measuring where the centre of the graph is but in different way. Mean is just a calculation of total percent mark per student but median is a percentile ranking.

. Rania Ali: Mean and median values are the same when there is a symmetry around the centre. So you can see that you can compare mean and median values to get such information.

Sonia: I guess mode will tell us something about one unique idea well developed in many students. I like that because it says that mode is like fashion. It relates to something unique.

Ms. Rania Ali: Mean, median and mode are all central tendencies. They can be used to compare different data and also learn more about them.

## Challange

**Compare CBSE Grade 12 and SAT results**

Here are graphs for Percentile Ranks vs. % Marks for CBSE Grade 12 exam vs SAT test. SAT or scholastic assessment test is a standardized from USA and it used for admissions to colleges in USA. When do the two graphs cross each other ? Do you think 20 percentile is going to be competitive enough for where you want to apply ? What do you find interesting in your comparison ?