Harmonic mean - practice problems - page 3 of 10
The harmonic mean is a type of average that is particularly useful for calculating rates, ratios, or situations involving reciprocals.It is calculated as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers.
The harmonic mean is often used when dealing with averages of quantities like speed, where time and distance are inversely related. It tends to be less affected by extremely large values in a dataset, making it more appropriate for skewed distributions compared to the arithmetic mean.
A key property of the harmonic mean is that it is always less than or equal to the arithmetic mean and the geometric mean for any set of positive numbers.
It is commonly applied in finance, such as calculating the average price-to-earnings ratio, and in physics, such as finding equivalent resistance in parallel circuits. The harmonic mean is not suitable for datasets containing zero or negative values, as it is undefined in such cases.
Number of problems found: 186
- Average speed
The car drove on one section of the highway for half an hour at a speed of 80 km/h. Then he reduced his speed to 60km/h. It went three-quarters of an hour at a speed of 60 km/h. What was the average speed of the car? - Treatment 46571
They have 3 sprayers for the chemical treatment of the vines. The first would spray the vineyard in 12 hours, the second in 15 hours, and the third in 10 hours. How long would it take to spray the vineyard with all the sprayers combined? - Workshops
The plant has three workshops. In the first workshop, produce five products/hour. In the second 8 products/hour, and in the third, seven products/hour. In the first workshop, they produced 240 products. In the second 400 and the third 350 products. Find t - Two cables
On a flat plain, two columns are erected vertically upwards. One is 7 m high, and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag.
- Truncated 43851
The pit is a regular truncated 4-sided pyramid, with 14 m and 10 m base edges and a depth of 6m. Calculate how much m³ of soil was removed when we dug this pit. - Solution 42531
What strong solution is created by mixing 3 liters of 30% solution and 2 liters of 70% solution? - Tributaries 40641
We would fill the water tank with one inflow in 3 hours and the other inflow in 2 hours. How long will it take for both tributaries to open? - Average speed
The car drove from city A to city B at 40 km/h and back to city A at a speed of 80 km/h. What was the average speed of the car? - 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
- Warehouse 36811
At the Prague Zoo, they need to know how long the fruit will last for the gorillas. The stock in the warehouse would last the female Kamba for 25 days, the male Richard for 20 days, and the little Nura even for 40 days. How long will the supply last if ev - Weighted harmonic average Ten workers will do some work in 2 minutes, five in 10 minutes, and three in 6 minutes. How many minutes per average worker per worker?
- Harmonic mean If x, y, and z form a harmonic progression, y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5.
- Harmonic series
Insert four members between 5/3 and 5/11 to form a harmonic series (means). - Insert 7
Insert five harmonic means between 3 and 18
Insert five harmonic means between 1/2 and 1/26
Find the harmonic mean of 4 and 8.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
