Class 9 Maths Statistics Grouped Frequency Distribution table

Grouped Frequency Distribution table

If you have score of lacs of students, then it is difficult to maintain the data in the Ungrouped Frequency Distribution table too, since the number of rows will be too high.

 

To present such a large amount of data so that a reader can make sense of it easily, we condense it into groups like 0-9, 10-19,20-29, 30-39, . . ., 90-99. These groupings are called ‘classes’ or ‘class-intervals’, and their size is called the class-size or class width, which is 10 in this case.

 

In each of these classes, the least number is called the lower class limit and the greatest number is called the upper class limit, e.g., in 20-29, 20 is the ‘lower class limit’ and 29 is the ‘upper class limit’.

Note that we can have any class size, we can create classes with size 20 or 25 or 30 also. Also note that in this case the classes are non- overlapping.

 

Let’s assume that we have score of 100 students

 

95 67 28 32 65 65 69 33 98 96 76 42 32 38 42 40 40 69 95 92 75 83 76 83 85 62 37 65 63 42 89 65 73 81 49 52 64 76 83 92 93 68 52 79 81 83 59 82 75 82 86 90 44 62 31 36 38 42 39 83 87 56 58 23 35 76 83 85 30 68 69 83 86 43 45 39 83 75 66 83 92 75 89 66 91 27 88 89 93 42 53 69 90 55 66 49 52 83 34 36

 

 

Since the minimum score in this case is 23, we will start with class 20-29. Presenting data in this form simplifies and condenses data and enables us to observe certain important features at a glance. This is called a grouped frequency distribution table.

 

Class size of non over lapping class is (Upper limit – Lower limit + 1).

So, in this case class size is 29-20 + 1  = 10

But creating non-overlapping class creates problem. Eg , in the case above we got students with score 29.5, 39.5 etc. We will not be able to include them in this list. So it is better to create overlapping class.

 

Eg: The distance (in km) of 40 engineers from their residence to their place of work were found as follows:   5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12. Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included).

Here let’s create a overlapping class.

 

Now the question is 5 lies in 2 classes, 0-5 & 5-10. In which class should be place 5.

By convention, in case overlapping class, 5 is placed in class 5-10, not in 0-5. The upper limit of the class is ignored & lower limit is considered.

 

Class size of over lapping class is (Upper limit – Lower limit).

So in this case class size is 5-0 = 5.

 

Note: Class size of non over lapping class is (Upper limit – Lower limit + 1).

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