Where does 40 go?

The idea

When observations are allotted to class-intervals, an observation equal to the upper class-limit of a class is counted in the next class.

Four students scored 40

30 students of Class X wrote a maths test out of 100. To study the marks, we sort them into classes of width 15: 10–25, 25–40, 40–55, …

Four students scored exactly 40. The number 40 is the end of one class and the start of the next.

Which class should those 4 students go in?

• 25–40
• 40–55
• Two of them in each class

Sort the marks into classes

Each chip is a mark and the number of students who got it, like 36 × 3. Drag it into the class where it belongs, or tap the chip and then the class. A wrong class sends it back and tells you why.

The upper limit belongs to the next class

An observation equal to the upper class-limit of a class is counted in the next class. So 40 marks go in 40–55, not in 25–40.

The class 25–40 holds the marks from 25 up to, but not including, 40. The class 40–55 starts with 40. This is the same rule you used to get the table of the 30 students: 2, 3, 7, 6, 6, 6.

Notes

An observation equal to the upper class-limit of a class is counted in the next class.

Check yourself

Heights are put in the classes 145–150 and 150–155. A girl is exactly 150 cm tall. Which class gets her?

Look at the marks you sorted. How many students are in the class 70–85?

Answer: 6

70 → 4 students, 72 → 1 student, 80 → 1 student. 4 + 1 + 1 = 6.

Eight students scored 20, 25, 30, 35, 40, 45, 50, 55. The classes are 20–30, 30–40, 40–50, 50–60. How many students are in 30–40?

Answer: 2

30 and 35 are in 30–40. 40 goes to 40–50. So the class has 2 students.

The class is 55–70. Which marks does it hold?

• 150–155 — correct. Yes! 150 is the upper limit of 145–150, so she is counted in the next class, 150–155.
• 145–150. The upper limit of 145–150 is 150, and a value equal to the upper limit goes to the next class.
• Both classes. Each observation is counted once. It goes in the next class, 150–155.
• 55 and 60, but not 70 — correct. Yes! 55 up to, but not including, 70. The mark 70 goes to the next class, 70–85.
• 55, 60 and 70. A mark of 70 is the upper limit, so it is counted in the next class.
• 60 and 70, but not 55. A mark of 55 is the lower limit of 55–70, so it is in this class. (It is the upper limit of 40–55, so it is not counted there.)