# Harmonic mean calculator

For harmonic mean calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 432.7 236.5 689.5 -808.2 953.0 957.1 -929.5 583.4 492.2 727.1 922.6 656.0 504.2**Harmonic mean**is the reciprocal of the arithmetic mean of the reciprocals.

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

Simple. First-type data elements (separated by spaces or commas, etc.), then type f: and further write frequency of each data item. Each element must have a defined frequency that count of numbers before and after symbol f: must be equal. For example:1.1 2.5 3.99

f: 5 10 15

### How to enter a grouped data?

Grouped data are data 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 |

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: type 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 be equal to the total for all observations since all frequencies will already have been added to the previous total.