# CLASS-9IMPORTANT TERMS RELATED TO GROUP DATA

Important Terms Related to Grouped Data

1) Class boundaries or True Upper and True Lower Limits:-

a) In the exclusive form, the upper and lower limits of a class are respectively known as the true upper limit and true lower limit.

b) In the inclusive form, the number midway between the upper limit of a class and the lower limit of the subsequent class gives the true upper limit of the class and the true lower limit of the subsequent class.

Thus, in the above table of inclusive form, we have :

10 + 11

The true upper limit of class 1 – 10 is (-----------) =  10.5

2

And, the true lower limit of class 11 – 20 is 10.5

Similarly,

20 + 21

The True upper limit of class 11 – 20 is (-----------) =  20.5

2

And, the true lower limit of class 11 – 30 is 20.5

Similarly,

30 + 31

The true upper limit of class 21 – 30 is (----------) =  30.5

2

And, the true lower limit of class 21 – 30 is 30.5

2) Class Size:-

The difference between the true upper limit and the true lower limit of a class will be called its class size.

True Upper Limit + True Lower Limit

3) Class Mark of A-Class = (----------------------------------)

2

The difference between any two successive class marks gives the class size.

Example: The class marks of a frequency distribution are 7, 13, 19, 25, 31, 37, 43. Find the class size and all the class intervals

Ans.) Class = Difference between two successive class marks = (13 – 7) = 6

Let the lower limit of the first class interval be x.

Then, its upper limit = (x + 6)

x + (x + 6)

So, -------------- = 7

2

=>      2x = 14 – 6

=>       x = 4

So, the first class interval is 4 – 10

Let, the lower limit of last class interval be y.

Then, its upper class limit = (y + 6)

y + (y + 6)

So, --------------- =  43

2

=>     2y = 86 – 6

=>       y = 40

So, the last class interval is 40 – 46

Hence the required class intervals are –

4 – 10, 10 – 16, 16 – 22, 22 – 28, 28 – 34, 34 – 40, 40 – 46.