Q 3.56. Explain the difference between t... [FREE SOLUTION]

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Chapter 3: Q 3.56. (page 105)

Explain the difference between the quantities $\underset{}{鈭�} x_{i} y_{i}$ and $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$ .Provide an example to show that, in general, those two quantities are unequal.

Short Answer

Expert verified

$\underset{}{鈭�} x_{i} y_{i} 鈮� (\underset{}{鈭�} x_{i}) (\underset{y_{i}}{鈭�})$

Step by step solution

Step 1. Given information.

$\underset{}{鈭�} x_{i} y_{i}$ and $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$

Step 2. The difference between ∑xiyi and ∑xi∑yi also provide an example to show that those two quantities are unequal

$\underset{}{鈭�} x_{i} y_{i}$ is the sum of products, where the individual corresponding values of two data sets are multiplied first, followed by the total sum.

$(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$ is a sum product, which means that the individual data sets are added separately and then the final sum of the two data sets is multiplied.

Consider the following set:

$(x_{i}) = 1, 2, 3, 4$ and $(y_{i}) = 4, 3, 2, 1$

role="math" localid="1652992532305" $\underset{}{鈭�} x_{i} y_{i} = (1 脳 4) + (2 脳 3) + (3 脳 2) + (1 脳 4) \underset{}{鈭�} x_{i} y_{i} = 4 + 6 + 6 + 4 \underset{}{鈭�} x_{i} y_{i} = 20$

And

role="math" localid="1652992556394" $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i}) = (1 + 2 + 3 + 4 +) (4 + 3 + 2 + 1) (\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i}) = (10) (10) (\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i}) = 100$

role="math" localid="1652992583289" $\underset{}{鈭�} x_{i} y_{i} 鈮� (\underset{}{鈭�} x_{i}) (\underset{y_{i}}{鈭�})$

As a result, $\underset{}{鈭�} x_{i} y_{i}$ is the product of sums and $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$ is the sum of sums.

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Explain the difference between the quantities $\underset{}{鈭�} x_{i} y_{i}$ and $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$ .Provide an example to show that, in general, those two quantities are unequal.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The difference between ∑xiyi and ∑xi∑yi also provide an example to show that those two quantities are unequal

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91影视

Explain the difference between the quantities 鈭�xiyiand 鈭�xi鈭�yi.Provide an example to show that, in general, those two quantities are unequal.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. The difference between ∑xiyi and ∑xi∑yi also provide an example to show that those two quantities are unequal

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Calculus

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Explain the difference between the quantities $\underset{}{鈭�} x_{i} y_{i}$ and $(\underset{}{鈭�} x_{i}) (\underset{}{鈭�} y_{i})$ .Provide an example to show that, in general, those two quantities are unequal.