Question

On the fee day, the amounts of fee collected from
20 students were as follows:
114, 108, 98, 100, 101, 109, 117, 119, 121, 126,
136, 143, 156, 169, 182, 195, 207, 219, 131,235
Represent the data in the form of a frequency
distribution table taking the class-intervals 90 -
120 (120 excluded), etc.​

Answer 1

Given :

• The amounts of the fee collected from 20 students.

To do :

• Represent the data in a frequency distribution table.

Answer :

$\small\boxed {\begin{array}{c|c|c} \underline{ \bf{Class \: interval}}& \underline{\bf{Tallymarks}}& \underline{ \bf{Frequency} }\\ \underline{ \sf{ \: \: \: \: \: \: 90 - 120 \: \: \: \: \: \: }}& \underline{\sf{ \: \: \: \: \: \cancel{||||} \: || | \: \: \: \: \: }}& \underline{ \sf{ \: \: \: \: \: \: \: 8 \: \: \: \: \: \: \: } }\\\underline{ \sf{ \: \: \: \: \: \: 120 - 150 \: \: \: \: \: \: }}& \underline{\sf \: \: \: \: \: \: \: { \cancel{ | || | } \: \: \: \: \: \: \: }}& \underline{ \sf{ \: \: \: \: \: \: \: 5 \: \: \: \: \: \: \: } } \\ \underline{ \sf{ \: \: \: \: \: \: 150 - 180 \: \: \: \: \: \: }}& \underline{\sf{ \: \: \: \: \: \: \: \: || \: \: \: \: \: \: \: \: }}& \underline{ \sf{ \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \: \: } } \\ \underline{ \sf{ \: \: \: \: \: \: 180 - 210 \: \: \: \: \: \: }}& \underline{\sf{ \: \: \: \: \: \: \: | || \: \: \: \: \: \: \: }}& \underline{ \sf{ \: \: \: \: \: \: \: \: 3 \: \: \: \: \: \: \: \: } } \\ \underline{ \sf{ \: \: \: \: \: \: 210 - 240\: \: \: \: \: \: }}& \underline{\sf{ \: \: \: \: \: \: \: \: \: || \: \: \: \: \: \: \: \: \: }}& \underline{ \sf{ \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \: \: } } \\ \\ \bf{total = }& \sf{}& \bf{20} \end{array}}$

Range of data :

• Maximum - Minimum = Range of data.
• 235 - 98 = range of data
• Range of data = 137

Know more :

• Each of the groups 0- 10, 10- 20, 20-30 etc. is called a Class Interval (or brieily a class).

• Now there is a possibility that10.occurs in both of the classes 0-10 and 10-20. To avoid this ambiguity the number that occurs in either of two consecutive classes is included in the 2nd one. For example, 10 will be considered in the class 10-20, not in 0-10, Similarly, 20 will occur in the class interval 20 30, but not in 10-20.

• For any class interval like 10- 20, 10 is called the lower limit and 20 the upper limit.

• The difference between the upper limit and lower limit is called as class width. For example, Class width of 0-10 is 10-0= 10; class width of 10-20 is 20- 10 10, etc. The class width in the above example is 10.