Weighted average - practice problems
A weighted average is a calculation where each value in a dataset is multiplied by a predefined weight before summing, reflecting its relative importance. Unlike a simple average, it accounts for variations in significance among data points, such as exam grades contributing differently to a final score. The formula divides the sum of weighted values by the sum of all weights. Common applications include academic grading, financial portfolios, and economic indices. It ensures more accurate results when data points have unequal influence.Directions: Solve each problem carefully. Show all your work.
Number of problems found: 119
- Journey 9
A person covers half of his journey at 40 km/h and the remaining half at 20 km/h. Find his average speed for the whole journey. - The first
The first 300 km of a journey is covered in 10/3 hours, and the remaining journey is covered in 8/3 hours at 75 km/h. Find the average speed of the whole journey. - Average cost
A man bought 1 dozen bananas at Rs 60 and 8 apples at Rs 120. What is the average cost of each? - A journey - 2 parts A part of journey is covered in 1 h 40 min at 75 km/h and the remaining part of it is covered in 2 h 50 min at 60 km/h. Find the total length of the journey and average speed.
- The rice 2
60 kg of a certain variety of rice at Rs 32 per kg is mixed with 48 kg of another variety of rice, and the mixture is sold at the average price of Rs 28 per kg. If there is no profit or loss due to the new sale price, then find the price of the second var - The mixture
If a 6-liter solution with a concentration of 20% alcohol is mixed with a 4-liter solution with a 60% concentration of alcohol. Find the percentage of alcohol in the mixture. - The average 11
The average of a set of 7 numbers is 20. The average of a second set of 13 numbers is 40. What is the mean of all 20? - Two classes
The average of 1 A class of 25 is 12 years, and the average age of 1B class of 22 is 10 years. What is the average age of the pupils of 1 A and 1B classes? - Suppose 12
Suppose in a physics test involving 30 students, and four scored 75%, eight scored 60%, twelve scored 50%, and six scored 30%. Calculate the mean of the group and the standard deviation. - Education - 5 modules In a self-paced online class, there are five modules. The first four modules are worth the same, but the fifth module is worth as much as the other four combined. A student is one-fourth of the way through the last module and has done one-third of three o
- Credit courses
A student takes a 5 credit course, a four-credit course, two three-credit courses, and a one-credit course. He gets a C in the five-credit course, a B in the four-credit course and one of the three-credit courses, and an A in the other three-credit course - Discrete and continuous
2,3,4,4,5,5,5,6,6,7 Assume the scores are measurements of a Discrete variable and find the median. Assume the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. - A potato
A potato farmer incurred a total cost of $1600 and $2500 from producing 5 and 8 potato bags, respectively, in 2 separate weeks. Find the cost of x bags. - The mean
The mean of four numbers is 5, and the mean of three different numbers is 12. What is the mean of the seven numbers together? - Runner 6
A runner runs the first lap of a circuit at an average speed of 5 km/h. At what speed must she run the second lap so that her average speed for both laps combined is 10 km/h? - Average time
Determine the weighted average time required in minutes per product, given that 6 workers each take 8 minutes, 15 workers each take 12 minutes, 5 workers each take 10 minutes, and 9 workers each take 13 minutes. - Tank - fuel prices
I have a car with a 50-litre tank. I want to calculate the weighted average price of a full tank of fuel at the end of the year. In December, 30 litres were filled at 37.50 CZK per litre, and in November, 40 litres at 38.40 CZK per litre. What is the weig - Good grades At school, 10 percent of boys and 15 percent of girls achieve good grades. What percentage of students achieve good grades when 60 percent of girls are in school?
- Pupils 22 Pupils of the graduating class at the Business Academy in Banská Bystrica had from the written test in Slovak language the following marks: 2, 2, 3, 3, 1, 4, 4, 2, 3, 5, 3, 3, 3, 4, 2, 4, 1, 1, 2, 3, 4, 5, 1, 3, 3, 2, 2, 3, 2, 1. Create a frequency distri
- CFO Director
The financial director has determined the following profitability scenarios for a new branch of the company: Profit of 5 million CZK with probability 0.1. Profit of 3 million CZK with probability 0.3. Profit of 1 million CZK with probability 0.4. Loss of
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