# Lower and upper fence calculator

For lower and upper fence calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 280.4 621.0 838.3 481.6 861.3 355.5 563.7 663.5 830.2 -387.4 734.4 615.2 237.2

### What is lower and upper fence?

The Lower fence is the "lower limit" and the Upper fence is the "upper limit" of data, and any data lying outside this defined bounds can be considered an outlier.

LF = Q1 - 1.5 * IQR
UF = Q3 + 1.5 * IQR

where Q1 and Q3 are the lower and upper quartile and IQR is the interquartile range.

### How to enter data as a frequency table?

Simple. Write data elements (separated by spaces or commas, etc.), then write f: and further write the frequency of each data item. Each element must have a defined frequency that counts numbers before and after symbol f: must be equal. For example:

1.1 2.5 3.99
f: 5 10 15

### How to enter grouped data?

Grouped data are formed by aggregating individual data into groups so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

 group frequency 10-20 5 20-30 10 30-40 15
This grouped data you can enter:
10-20 20-30 30-40
f: 5 10 15

### How to enter data as a cumulative frequency table?

Similar to a frequency table, but instead, f: write cf: in the second line. For example:

10 20 30 40 50 60 70 80
cf: 5 13 20 32 60 80 90 100

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always equal the total for all observations since the calculator will have already added all frequencies to the previous total.