# Harmonic mean calculator

For harmonic mean calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 329.3 737.7 137.6 637.8 996.5 483.6 432.1 702.3 762.4 681.7 -658.1 453.2 803.3**Harmonic mean**is the reciprocal of the arithmetic mean of the reciprocals.

### 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 |

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.

## Practice problems from statistics:

- Harmonic HM example

Find the harmonic mean of 4 and 8. - Harmonic and arithmetic means

The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculate: a - A frequency

A frequency table of grades has five classes (A, B, C, D, F) with frequencies of 2,14,13,8, and 1, respectively. Using percentages, what are the relative frequencies of the five classes? - Carpenters

Carpenters 1 and 2 spend ten days and five days respectively to make one table. The first carpenter and 30 made 50 tables by the second. What is the average time spent on the products? - Harmonic 4

Find the harmonic mean of -6 and 5. - Statistical survey

Write TRUE OR FALSE for each question: 1 Standard deviation measures central location. 2. The most frequent observation in a data set is known as the mode. 3 The most passive method of data collection is observation. 4 Access time for secondary data is sh - HP - harmonic progression 2

Compute the 16th term of the HP if the 6th and 11th terms of the harmonic progression are 10 and 18, respectively. - Harmonic series

Insert four members between 5/3 and 5/11 to form harmonic series (means). - HP - harmonic progression

Determine the 10th term of the harmonic progression 6,4,3,… - Two painters

Two painters are assigned to finish painting the houses in a housing project. John can finish a house in 4 days. Kurt painted it in 3 days. How long would it have taken if John and Kurt worked painting the house together? - Insert 5

Insert five harmonic means between 1/2 and 1/26

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