Harmonic Mean Calculator

What is harmonic mean in statistics?

The harmonic mean is one of the several types of “mean”. It is the reciprocal of the arithmetic mean. To calculate it we usually divide the sum of the reciprocals of all values by the total number of terms.

Formula of Harmonic mean:

Generally, for the ungroup data we use the following formula:

Harmonic mean formula

In the above formula:

“Σ (1 / X_i)” is the sum of reciprocals of all values
“n” is the total number of terms

How to Calculate Harmonic Mean?

Below examples are solved to calculate the harmonic mean of any ungroup data.

Example 1:

Evaluate the harmonic mean of the following data:

1, 5, 7, 3, 9, 12, 13

Solution:

Step 1: Extract the data

Let X = 1, 5, 7, 3, 9, 12, 13

Total number of terms = n = 7

Step 2: Put the values in the formula.

Harmonic mean = n / Σ (1 / X_i)

Harmonic mean = 7 / (1 / 1 + 1 / 5 + 1 / 7 + 1 / 3 + 1 / 9 + 1 / 12 + 1 / 13)

Harmonic mean = 7 / (1 + 0.2 + 0.1429 + 0.3333 + 0.1111 + 0.0833 + 0.0769)

Harmonic mean = 7 / 1.9475

Harmonic mean = 3.59424

Example 2:

If a person is driving a car at the rate of 50 km/h during the first 30 kilometers, 60 km/h during the 2^nd 30 kilometers, 90km/h during the 3^rd 30 kilometers, and 100km/h during the 4^th 30 kilometers calculate the average speed of the car.

Solution:

Step 1: Extract the data

Let,

Speed of car = X = 50, 60, 90, 100

Total number of terms = n = 4

Step 2: Put the values in the formula.

Harmonic mean = n / Σ (1 / X_i)

Harmonic mean = 4 / (1 / 50 + 1 / 60 + 1 / 90 + 1 / 100)

Harmonic mean = 4 / (0.02 + 0.0167 + 0.0111 + 0.01)

Harmonic mean = 4 / 0.0578

Harmonic mean = 69.23077

Recent Blogs

Related Tools

1. Standard Deviation Calculator

2. Variance Calculator

3. Coefficient of Variation Calculator

4. Covariance Calculator

5. Correlation Coefficient Calculator

6. Mean Calculator

7. Median Calculator

8. Mode Calculator

9. Mean Absolute Deviation Calculator

10. Arithmetic Mean Calculator

11. Geometric Mean Calculator

12. Sum of Squares Calculator

13. Quartile Calculator

14. Quadratic Regression Calculator

15. Linear Regression calculator

16. Expected Value Calculator

17. Hypergeometric Distribution Calculator

18. Anova Calculator

19. Five Number Summary Calculator

20. Z Score Calculator

21. P Value Calculator

22. Critical Value Calculator

23. Chebyshev's Theorem Calculator

24. Pie Chart Maker

25. Poisson Distribution Calculator

26. T Test Calculator

27. Degrees of Freedom Calculator

28. Chi Square Calculator

29. Sample Size Calculator

30. Decile Calculator

31. Probability Calculator

32. Normal Distribution Calculator

33. Margin of Error Calculator

34. Confidence Interval Calculator

35. Descriptive Statistics Calculator

36. Histogram Maker

37. Standard Error Calculator

38. Scatter Plot Maker

39. Outlier Calculator

40. Coefficient of Determination Calculator

41. Binomial Distribution Calculator