Harmonic mean - practice problems - page 4 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
- HP - harmonic progression
Determine the 10th term of the harmonic progression 6,4,3,… - Statistics quiz
Fill in the missing word. 1. in a data set, the mean, median, and mode are measured of ________________ 2. "The manipulation of variables under controlled conditions" is the data collection method known as______________ 3. in a normal distribution, the ar - The leaves
Karel raked the leaves in the garden alone in 24 minutes, and his younger brother took 30 minutes. How long would they dig a garden if Karel digs alone for 6 minutes and his brother comes to his aid? - Together 28411
Worker A will dig a trench in 12 days. Worker B will dig a trench in 18 days. How many days will it take them together?
- Cleaning 27663
During the pool cleaning, two drains and one inlet were opened. The first outflow would empty the pool in 6 hours, the second outflow would fill it in 9 hours, and the inflow would fill it in 12 hours. How long will it take to empty if the drains are open - Production 24021 The plant has to complete the order in 40 working days. Production takes place in two workshops. In the first one, there are more workers; therefore, they would complete the order themselves in 70 working days. In the second workshop, they would complete
- Performance 20233
How much percent performance improvement is needed if the work we have planned for five days has to be managed in three days? - Calculate 19023
A car traveled from city A to city B at a speed of 40 km/h, then from B to C at 60 km/h, and finally from C to D at 50 km/h. Calculate the car's average speed over the entire route from A to D if the distance from A to B is 20% of the total distance and f - Simultaneously 17821
The reservoir is filled with the first pump in 30 hours, the second in 24 hours, and the third in 20 hours. How long does it take to fill the reservoir if all pumps are switched on simultaneously?
- Aircraft angines
The aircraft's two engines are enough to supply the fuel for five hours of operation. However, one of the engines has malfunctioned and thus consumes one-third more fuel. How long can the plane be in the air before it runs out of fuel? After an hour of ma - Water current
John swims upstream. After a while, he passes the bottle, and from that moment, he floats for 20 minutes in the same direction. He then turns around and swims back, and from the first meeting with the bottle, he sails 2 kilometers before he reaches the bo - Panel house
The construction company has two groups of workers. Group A has more members than B. The Panel house was insulated by group A for ten days. They insulated the same block of flats together for 6 days. How many days would group B block insulate? - Birdhouse 12941
Michal would make a birdhouse in three hours, and Richard would make it in two hours. If they work together, how many hours will it take them to complete it? How much percent more time compared to the time of working together would Michal make the booth b - Independently 12921
Factory A can fulfill the order independently in 10 days. Factory B fulfills the same order in 16 days. How many days will the order be completed if only plant B works on it for 3 days and then both plants together?
- Mixture of nuts
We should prepare the mixture of nuts from almonds, peanuts, and nuts cashew ratio of 1:2:3 (respectively). The price of almonds is 150 CZK/kg, the price of peanuts is 140 CZK/kg, and the price of cashew nuts is 180 CZK/kg. The price of the mixture is det - Between two bus stops
Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that he would have arrived at the bus stop if he had run to one or the other. The average bus speed is 60 km/h. What is Wanda's average running spee - Average speed
The truck drove 1/2 of the way on the highway at 80 km/h. The other half of the way, 20 km/h. Calculate the average speed. - Two parts journey The car driver plans to drive to a distance of 30 km in 0.5 hours. For twenty minutes, he follows the column at a speed of 30 km/h. What speed would he have to go in the remaining time?
- Motorcyclist 8671
The motorcyclist was riding: a) the first half of the driving time at a speed of 30 km/h, the second half of the time at a speed of 60 km/h, b) the track's first half at a speed of 30 km/h and the second half at a speed of 60 km/h. Determine its average s
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
