One number for a whole class
The class mark is the middle of the class.
Seven students in one class
In the table of 30 students, 7 students scored in the class 40–55. We do not know their exact marks any more. We only know each one is in 40–55.
To work with the class, we want one number that stands for all 7 students.
Which number would you choose to stand for the class 40–55?
What this lesson covers
The idea
Each class is represented by its mid-point or class mark = (Upper class limit + Lower class limit)/2, assuming that the frequency of the class is centred around its mid-point.
Seven students in one class
In the table of 30 students, 7 students scored in the class 40–55. We do not know their exact marks any more. We only know each one is in 40–55.
To work with the class, we want one number that stands for all 7 students.
Which number would you choose to stand for the class 40–55?
- 40, the lower limit
- 47.5, the middle
- 55, the upper limit
Find the middle of each class
The red bar is the gap from the lower limit to the marker, and the green bar is the gap from the marker to the upper limit. Move the marker (the − and + buttons move it by 0.5) until the two gaps are equal. Do it for every class.
The class mark
Class mark = (Upper class limit + Lower class limit)/2. It is the mid-point of the class.
We assume that the frequency of a class is centred around its mid-point: all the students of the class are treated as if they stand at the class mark. For 10–25 the class mark is (10 + 25)/2 = 17.5.
Notes
Class mark = (Upper class limit + Lower class limit)/2. All the students of a class are treated as if they stand at its class mark.
Check yourself
Find the class mark of the class 25–40.
Answer: 32.5
(25 + 40)/2 = 65/2 = 32.5.
The percentage of female teachers in the schools of some states lies in the class 15–25 (NCERT Example 2). Find its class mark.
Answer: 20
(15 + 25)/2 = 40/2 = 20.
Bowlers are grouped by the number of wickets they took. Find the class mark of the class 100–150 (NCERT Example 3).
Answer: 125
(100 + 150)/2 = 250/2 = 125.
The class 40–55 has 7 students. When we work with the class mark, we treat each of those 7 students as if he or she scored…
- 47.5 — correct. Yes! 47.5 is the class mark of 40–55, and every student of the class is treated as standing there.
- 40. 40 is the lower limit. The class mark is the middle of the class.
- 55. 55 is the upper limit, and a mark of 55 would even belong to the next class. The class mark is the middle.