3.2 Grouped frequency tables
You have already seen data presented in grouped frequency tables:
| Age (in years) | 0 - 4 | 5 - 10 | 11 - 17 | 18+ |
| Number of people | 73 | 107 | 0 | 1320 |
| Age group | Number of village residents |
| 0 – 16 | 180 |
| 17 – 20 | 96 |
| 21 – 40 | 630 |
| 41 – 60 | 414 |
| 61+ | 180 |
| TOTAL | 1500 |
These are both examples of grouped frequency tables. The age range is divided into groups, or intervals, and the number of people (frequency) in each group has been recorded.
As mentioned in Week 1, it is important that the groups do not overlap. For continuous data, inequality signs should be used to represent each group precisely. In the next activity you will need to know that < means ‘less than’ and ≤ means ‘less than or equal to’.
Activity 8 Grouping data
Here is a list of some (continuous) data about the length of time in minutes it would take some village residents to walk to the site of the proposed play park.
| 12 | 12 | 14 | 2 | 15 |
| 5 | 1 | 2 | 10 | 57 |
| 25 | 28 | 43 | 30 | 19 |
Complete the grouped frequency table below to organise this data.
| Time (t) in minutes | Tally | Frequency | |
| 0 < t ≤ 5 | |||
| 5 < t ≤ 10 | |||
| 10 < t ≤ 20 | |||
| 20 < t ≤ 30 | |||
| 30 < t ≤ 60 | |||
| TOTAL |
Table 5 Time taken by a sample of village residents to walk to the play park site
When tallying data, it is helpful to strike through values as you tally them to ensure no values are missed. This means tallying data presented on a screen can be more error prone; something worth thinking about if providing pupils in a class with listed data projected on a screen.
Comment
The completed frequency table should look like this:
AP to add tally below for ‘5’ Maybe as an image file(?)| Time (t) in minutes | Tally | Frequency |
| 0 < t ≤ 5 | |||| | 4 |
| 5 < t ≤ 10 | | | 1 |
| 10 < t ≤ 20 | 5 | |
| 20 < t ≤ 30 | ||| | 3 |
| 30 < t ≤ 60 | || | 2 |
| TOTAL | 15 |
Table 6 Time taken by a sample of village residents to walk to the play park site (completed)
Some learners do not like grouping data. They may feel they are losing information. It is true that if you do not know the exact data values, then the results of any statistical calculations would be estimates and not exact. However, this is reasonable as your data is variable – it is likely to be a sample of the overall population, and every sample would likely produce different results. There may also be potential issues with the data such as some answers being recorded or interpreted incorrectly.
In statistics you are trying to get a good overall sense of the data or information rather than trying to collect and record every individual result perfectly.
In Week 3 you will look at calculating some statistics on collected data however, for this course, we will not be covering how to perform these calculations with grouped data such as that discussed here. We have already alluded to the fact that any statistical calculations performed on such data would be estimates. When performing calculations on data that has been grouped, it is common to take the value of the midpoint of the group to represent every data item in that group.