# Isn't it should be equal and more than the lower bound but less than the upper bound?

For frequency distribution for numeric variable between 1 and 100 both inclusive, the split / interval is

(1, 21]

(21, 41]

(41, 61]

where the number is included in the interval if it is equal to or more than the lower bound but less than the upper bound

so if the number is 1 it will be in first interval and if the number is 21 then it will be in second interval, right?

Hi Nisrin,

I think also this is an error.

I would use this notation for the intervals:

[1, 21[ (21 not included in the first interval)

[21, 41[

[41, 61[

[61, 81[

[81, 101[

Hi Benjoun,

Seriously I have no information of open square bracket usage in frequency distribution.

Rule is open parenthesis (round bracket) before lower bound that is included and closing square bracket after the upper bound that is excluded.

Thanks

The image you've provided shows a frequency distribution table with intervals for grouping the data. The intervals are listed as:

1 to 21

21 to 41

41 to 61

61 to 81

81 to 101

The issue with these intervals is that they overlap. For example, a value of 21 could belong to either the first interval (1-21) or the second interval (21-41). This could cause confusion when assigning frequencies to the intervals because each data point should belong to one and only one interval.

Typically, intervals are designed to be mutually exclusive and exhaustive. This means that every data point should fit into one and only one interval without any ambiguity. The intervals should be adjusted to avoid overlap, perhaps like this:

1 to 20

21 to 40

41 to 60

61 to 80

81 to 100

Alternatively, if you wish to include the upper bound, you might use a bracket notation to indicate that the upper bound is included in the interval, while the lower bound of the next interval is not. Here’s how it might look:

[1, 20]

(20, 40]

(40, 60]

(60, 80]

(80, 100]

In this notation, the round bracket (( indicates that the number is not included in the interval, while the square bracket [[ indicates inclusion. This way, the number 20 is included in the first interval but not in the second, and so on. However, this approach is less common in simple frequency distribution tables, and the first adjustment I suggested is typically clearer for most purposes.

@Isaac I agree with your comment.