Geometric Mean vs Arithmetic Mean: Real-Life Applications

A gardener wants to find the average height of two types of plants. Type A plants are 4 feet tall and Type B plants are 16 feet tall. What is the geometric mean of their heights?

• 8 feet

• 12 feet

• 6 feet

• 10 feet

In a class, the scores of two students in a math test are 25 and 100. Calculate the geometric mean of their scores and compare it to the arithmetic mean.

• Geometric mean: 50, Arithmetic mean: 62.5

• Geometric mean: 100, Arithmetic mean: 62.5

• Geometric mean: 75, Arithmetic mean: 80

• Geometric mean: 25, Arithmetic mean: 50

A car travels 60 miles per hour for 2 hours and then 90 miles per hour for 1 hour. What is the geometric mean speed of the car during the trip?

• 80 miles per hour

• 70 miles per hour

• 75 miles per hour

• 65 miles per hour

A student recorded the number of books read over three months: 2, 8, and 32. What is the geometric mean of the number of books read?

• 10

• 8

• 24

• 16

Two friends are comparing their weekly earnings. One earns $200 and the other earns $800. What is the geometric mean of their earnings, and how does it compare to the arithmetic mean?

• The geometric mean is 400, which is less than the arithmetic mean of 500.

• The geometric mean is 300, which is less than the arithmetic mean of 400.

• The geometric mean is 500, which is equal to the arithmetic mean of 500.

• The geometric mean is 600, which is greater than the arithmetic mean of 500.

A researcher measures the growth of bacteria in two different environments: 10 and 90 bacteria. What is the geometric mean of the bacteria counts?

• 100

• 30

• 50

• 20

A cyclist rides 12 miles in the first hour and 48 miles in the second hour. What is the geometric mean of the distances covered in each hour?

• 18

• 36

• 24

• 30

In a science experiment, the weights of two samples are 3 kg and 27 kg. Calculate the geometric mean of the weights and compare it to the arithmetic mean.

• Geometric mean: 10 kg; Arithmetic mean: 18 kg. Geometric mean is greater than arithmetic mean.

• Geometric mean: 15 kg; Arithmetic mean: 9 kg. Geometric mean is greater than arithmetic mean.

• Geometric mean: 9 kg; Arithmetic mean: 15 kg. Geometric mean is less than arithmetic mean.

• Geometric mean: 12 kg; Arithmetic mean: 20 kg. Geometric mean is equal to arithmetic mean.

A store sells two types of shoes: one for $30 and another for $90. What is the geometric mean price of the shoes?

• 75.00

• 60.00

• 51.96

• 45.00

A student wants to find the average of two test scores: 50 and 200. What is the geometric mean of the scores, and how does it compare to the arithmetic mean?

• The geometric mean is 125, which is greater than the arithmetic mean of 100.

• The geometric mean is 75, which is equal to the arithmetic mean of 125.

• The geometric mean is 150, which is less than the arithmetic mean of 200.

• The geometric mean is 100, which is less than the arithmetic mean of 125.