ungrouped data - comprehensive study approach

In statistics, data items can be considered as a group instead of considering an individual item especially when the number of records are huge.

In grouping, you take few neighboring items and put them in a group, for example if you have items like 41,42,42,43,45,46, you can decide to consider a group of 41-45 instead of listing the numbers individually.

Let us consider the data provided below that represents ages of some 20 senior workers in a company:

63, 53, 58, 64, 54, 64, 58, 67, 54, 54, 56, 53, 51, 52, 58, 53, 63, 65, 67, 58.

we can make the frequency table as we discussed earlier

Age	Tally	Frequency
51	/	1
52	/	1
53	////	4
54	//	2
56	/	1
58	////	4
63	//	2
64	//	2
65	/	1
67	//	2
Total	summation	20

ungrouped data of senior workers in a company

63, 53, 58, 64, 54, 64, 58, 67, 54, 54, 56, 53, 51, 52, 58, 53, 63, 65, 67, 58.

We can reduce the size of the table by grouping the data in 5 values as shown. please note that we have changed the first column from age to class meaning it will represent a class of a certain age group.

class	Tally	Frequency
51-55	~~////~~ ///	8
56-60	~~////~~	5
61-65	~~////~~	5
66-70	//	2
Total	summation	20

Grouped data for senior workers in a company

Measurements such as height, mass, age, time e.t.c are usually estimates of the actual values therefore any value between 50.5 and 51.4 could be estimated as 51. Therefore we can write interval x as 50.5 ≤x< 51.5.

A class interval 51-55 includes all masses between 50.5 t0 55.5

The values 50.5 and 55.5 are called the class boundaries of the class 51-55.

50.5 is the lower class boundary in this case and 55.5 is the upper class boundary.

The difference between the class boundaries is the class width(class size). For example in the example above, class width =55.5-50.5 = 5

when grouping data, ensure the groups are not so many, the most recommended is 5-12 groups.

practice question

The data below shows masses of 30 animals in animal farm.

27, 28, 24, 25, 30, 40, 30, 28, 26,43, 27, 28, 33, 35, 36, 27, 30, 28, 31, 30, 28, 29, 30, 35, 32, 26, 25, 42, 43, 27.

Required:

(a) Make a grouped frequency table for the data

(b) represent the grouped data in a bar graph and then in a pie chart4

Solution

The first step is deterring the number of classes. This we do by determining the range and the size of each group. let say each group should have n items and the range is R.

The number of groups (classes=R/n) approximated to the nearest whole number that is greater than R/n.

the range is the difference between the highest score and the lowest score. In the above data, the range = 43-24 = 19

Assuming we want each class has five items, then number of classes = 19/5≈3.8 which should be 4 to the nearest whole number. however we said the best numbers is between 5-12. hence we can reduce the number of items per group, probably to 4.

hence 19/4 = 4.75 classes ≈5

five classes are better than four because fewer number of items in a group can increase accuracy when calculating the measures of central tendencies.

the groups starts from the lowest value, and then add 3 items to get the upper boundary of that group. Note we have added 3 and not 4 because the lower boundary need 3 more items to make 4 items in the group.

The frequency table for the grouped data should be as follow

classes	Tally	Frequency
24-27	~~////~~ ////	9
28-31	~~////~~ ~~////~~ //	12
32-35	////	4
36-39	/	1
40-43	////	4
Total	summation	30

Frequency table for masses of animals in a farm

The data can be represented in the in a bar graph as shown

Practice question

The marks obtained by students in a Java test were recorded as follow

71, 73, 64, 58, 49, 52, 62, 68, 52, 48, 55, 63, 60, 71, 66, 61, 58, 57, 65, 64, 49, 52, 59, 53, 59, 74, 56, 57, 59,66.

required:

make a frequency distribution table for the data
Draw a histogram to show this information

Tag: ungrouped data

Grouped and Ungrouped data

practice question

Required:

Solution

Practice question

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