STA 202 : ASSIGNMENT 1. Which of the following is the formula for the arithmetic mean of ungrouped data? A. n / ∑(1/X) B. (∑X)^(1/n) C. (∑X) / n D. ∑X × n 2. The sum of 10 numbers is 250. What is their arithmetic mean? A. 20 B. 25 C. 30 D. 35 3. Find the arithmetic mean of 12, 18, 24, 30, 36. A. 20 B. 22 C. 24 D. 26 4. The arithmetic mean of 6 numbers is 13. What is their total sum? A. 78 B. 68 C. 80 D. 72 5. The mean of 4 numbers is 25. Three numbers are 20, 30, and 28. Find the fourth number. A. 22 B. 24 C. 26 D. 28 6. Which measure of central tendency is the nth root of the product of n observations? A. Arithmetic Mean B. Geometric Mean C. Harmonic Mean D. Median 7. Find the geometric mean of 9 and 16. A. 10 B. 11 C. 12 D. 13 8. Find the geometric mean of 3, 6, 12. A. 6 B. 7 C. 8 D. 9 9. The geometric mean of two numbers is 15 and one number is 9. Find the other. A. 20 B. 25 C. 30 D. 35 10. Find the geometric mean of 1, 4, 16, 64. A. 4 B. 6 C. 8 D. 10 11. Which mean is most appropriate for averaging speeds over equal distances? A. Arithmetic Mean B. Geometric Mean C. Harmonic Mean D. Median 12. Find the harmonic mean of 3 and 6. A. 3 B. 4 C. 5 D. 6 13. Find the harmonic mean of 4, 8, 12. A. 6.55 B. 6.86 C. 7.0 D. 7.2 14. The harmonic mean of two numbers is 9.6 and one number is 12. Find the other. A. 6 B. 8 C. 10 D. 14 15. Find the harmonic mean of 10, 20, 40. A. 15.5 B. 16.0 C. 17.14 D. 18.0 16. The arithmetic mean of two numbers is 10 and their geometric mean is 8. Find the numbers. A. 4 and 16 B. 5 and 15 C. 6 and 14 D. 8 and 12 17. The geometric mean of three numbers is 6. Two numbers are 3 and 12. Find the third. A. 6 B. 9 C. 12 D. 18 18. The harmonic mean of three numbers is 6. Two numbers are 4 and 12. Find the third. A. 6 B. 8 C. 10 D. 12 19. Which mean is always less than or equal to the geometric mean for positive numbers? A. Arithmetic Mean B. Harmonic Mean C. Both A and B D. None 20. If the arithmetic mean and harmonic mean of two numbers are 10 and 6.4 respectively, find the geometric mean. A. 7 B. 8 C. 9 D. 10
This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.
ScanSolve AI Answer
Here are the solutions to your assignment questions:
1. C. $\frac{\sum X}{n}$
Step 1: The arithmetic mean for ungrouped data is calculated by summing all the observations and dividing by the number of observations.
$$ \text{Arithmetic Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} = \frac{\sum X}{n} $$
The correct formula is $\boxed{\frac{\sum X}{n}}$.
2. B. 25
Step 1: Identify the given values.
Number of numbers ($n$) = 10
Sum of numbers ($\sum X$) = 250
Step 2: Apply the formula for the arithmetic mean.
$$ \text{Arithmetic Mean} = \frac{\sum X}{n} $$
$$ \text{Arithmetic Mean} = \frac{250}{10} $$
$$ \text{Arithmetic Mean} = 25 $$
The arithmetic mean is $\boxed{25}$.
3. C. 24
Step 1: Identify the given numbers and count them.
Numbers: 12, 18, 24, 30, 36
Number of observations ($n$) = 5
Step 2: Calculate the sum of the numbers.
$$ \sum X = 12 + 18 + 24 + 30 + 36 = 120 $$
Step 3: Apply the formula for the arithmetic mean.
$$ \text{Arithmetic Mean} = \frac{\sum X}{n} $$
$$ \text{Arithmetic Mean} = \frac{120}{5} $$
$$ \text{Arithmetic Mean} = 24 $$
The arithmetic mean is $\boxed{24}$.
4. A. 78
Step 1: Identify the given values.
Number of numbers ($n$) = 6
Arithmetic Mean ($\bar{X}$) = 13
Step 2: Use the formula for the arithmetic mean to find the total sum.
$$ \bar{X} = \frac{\sum X}{n} $$
$$ \sum X = \bar{X} \times n $$
$$ \sum X = 13 \times 6 $$
$$ \sum X = 78 $$
The total sum is $\boxed{78}$.
5. A. 22
Step 1: Identify the given values.
Number of numbers ($n$) = 4
Mean ($\bar{X}$) = 25
Three numbers: 20, 30, 28
Step 2: Calculate the total sum of the 4 numbers.
$$ \sum X = \bar{X} \times n $$
$$ \sum X = 25 \times 4 $$
$$ \sum X = 100 $$
Step 3: Sum the three
