## 3.1 Frequency, relative frequency, and cumulative tables for numerical data

In order to create frequency tables for numerical data, there is one preliminary step we need to take that was not necessary for categorical data. Consider the variable Height, which contains the height of each student in centimeters. Since Height is a numeric, continuous variable, there are no obvious categories for us to present in a frequency table. We can, however, group the data into suitable ranges. These ranges should be equal, non-overlapping intervals. For example, the below table presents the number of students in each 5cm range:

Table 3.1: Frequency table detailing students` heights.
Height (cm) Frequency
[150,155) 6
[155,160) 13
[160,165) 20
[165,170) 45
[170,175) 42
[175,180) 27
[180,185) 28
[185,190) 17
[190,195) 8
[195,200) 2
[200,205) 1

Note that the square brackets "[" mean that the interval includes that particular number, whereas the round brackets ")" mean that the interval goes all the way up (or down) to, but does not include, that particular number. For example, the interval [195, 200) starts at (and includes) 195, and goes all the way up to, but does not include, 205. This means that the intervals do not overlap.

Using what we learnt earlier, we can extend the above table to also include relative and cumulative frequencies:

Table 3.2: Complete table for height survey data.
Height Frequency Cumulative Frequency Relative Frequency (%) Cumulative Relative Frequency (%)
[150,155) 6 6 2.87 2.87
[155,160) 13 19 6.22 9.09
[160,165) 20 39 9.57 18.66
[165,170) 45 84 21.53 40.19
[170,175) 42 126 20.10 60.29
[175,180) 27 153 12.92 73.21
[180,185) 28 181 13.40 86.60
[185,190) 17 198 8.13 94.74
[190,195) 8 206 3.83 98.56
[195,200) 2 208 0.96 99.52
[200,205) 1 209 0.48 100.00