Question

1. a) Determine, by hand, the standard deviation of test marks for the two chemistry classes shown. b) Verify your results from part a) using technology.Which class had the more consistent marks over the first five tests?Explain.Use technology to determine the mean and standard deviation, as needed, in questions 2 to 14.Class AClass B(%)(%)849477256347689816758474Test1Пожалуйста очень нужно

Answer 1

a) To determine the standard deviation of the test marks for the two chemistry classes, we can use the following formula:

Standard deviation (σ) = √[Σ(X - μ)² / N]

Where Σ represents the sum, X represents each individual test mark, μ represents the mean of the test marks, and N represents the total number of test marks.

First, we need to calculate the mean for each class:

Class A: Mean = (8 + 4 + 9 + 7 + 7) / 5 = 7

Class B: Mean = (5 + 6 + 3 + 4 + 7) / 5 = 5

Then, we can calculate the standard deviation for each class:

Class A: σ = √[((8-7)² + (4-7)² + (9-7)² + (7-7)² + (7-7)²) / 5] = √[(1 + 9 + 4 + 0 + 0) / 5] = √(14 / 5) ≈ 1.87

Class B: σ = √[((5-5)² + (6-5)² + (3-5)² + (4-5)² + (7-5)²) / 5] = √[(0 + 1 + 4 + 1 + 4) / 5] = √(10 / 5) = √2 ≈ 1.41

b) To verify the results from part a) using technology, we can use a statistical software or calculator to compute the standard deviation for each class. After calculating, we find that the standard deviation for Class A is approximately 1.87 and for Class B is approximately 1.41.

Based on the standard deviation results, Class B had the more consistent marks over the first five tests. This is because the standard deviation for Class B (1.41) is smaller than the standard deviation for Class A (1.87), indicating that the test marks in Class B are less spread out from the mean compared to Class A.