DzaWeb: Ungrouped frequency distribution

When the range of the data values is relatively small, a frequency distribution can be constructed using single data values for each class. This type of distribution is called ungrouped frequency distribution. This of data is organised in such a way that the marks are not grouped.

Example one (1)

Marks	1	2	3	4	5	6	7	8
Frequency	2	7	5	4	9	7	6	5

Example two (2)

Age (yrs)	Frequency
17	3
18	10
19	8
20	5
21	2

Processing Ungrouped Frequency Distribution:

NB: [Processing Raw Data – case one]:

The following data represent the visitors to a museum for 50 days

41 52 46 42 46 36 44 68 58 44

49 48 48 62 52 50 45 72 45 43

63 49 57 44 48 49 45 47 48 43

45 56 61 54 51 47 42 53 41 54

58 55 43 63 38 42 43 46 49 47

Using intervals 35 – 39, 40 – 44 etc form a frequency distribution table for the data.

NB: Depending on the question asked ALL OR SOME of the entries in the table below are required.

NB: [Processing Raw Data – case two]:

Sometimes students are required to process a raw data without a GIVEN INTERVAL. Care must be taken in such cases, for most of them can easily be processed as an UNGROUPED DATA instead of a GRUOPED DATA. For certainty, check the range of the data. That is the lower figure and the highest figure. If the range is short and the figures are consecutive in nature, then the data can be processed as an ungrouped data.

For example the following data shows marks obtained by students in a mathematics test.

6 9 5 9 5 3 6 6 7 6

7 5 5 2 7 10 5 6 4 6

2 9 8 0 6 2 9 7 1 8

Construct a frequency table for the data.

NB: [Processing Raw Data – case three]:

If the range is wide and the figures are not consecutive in nature, the data is best processed as grouped data. In such cases, intervals chosen should be such that the number of class intervals would be between 5 and 13 in order to minimize errors.

For example, the following table gives the marks of 30 students in a class.

45 68 67 61 59 59 59 60 64 65

68 71 69 67 64 63 50 62 64 64

76 57 68 55 72 53 80 74 70 57

Solution

NB: The highest figure is 80 and the lowest is 45. If we select class intervals of width 10, we have only five classes, which is not the best. However, if we go for class interval of width 5, we have about 8 classes which are between 5 and 13 classes as stated above. We therefore go for the width of 5. Now,

Marks	Class Midpoint	Tally	Frequency
45 – 49	47	/	1
50 – 54	52	///	3
55 – 59	57	//// /	6
60 – 64	62	//// //	7
65 – 69	67	//// /	6
70 – 74	72	////	4
75 – 79	77	//	2
80 - 84	82	/	1