Q 3.55. Explain the difference between t... [FREE SOLUTION]

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Chapter 3: Q 3.55. (page 105)

Explain the difference between the quantities ${(\underset{}{鈭�} x_{i})}^{2}$ and $\underset{}{鈭�} {x^{2}}_{i}$ Construct an example to show that in general those two quantities are unequal.

Short Answer

Expert verified

${(\underset{}{鈭�} x_{i})}^{2} 鈮� \underset{}{鈭�} {x_{i}}^{2}$

Step by step solution

Step 1. Given information.

${(\underset{}{鈭�} x_{i})}^{2}$ and $\underset{}{鈭�} {x^{2}}_{i}$

Step 2. The difference between ∑xi2 and ∑x2i also construct an example to show that those two quantities are unequal

${(\underset{}{鈭�} x_{i})}^{2}$ is the square of sums, which means that all of the values in the data set are added first, and then the total sum is squared.

$\underset{}{鈭�} {x^{2}}_{i}$ is the sum of the squares, where each data set value is squared and then added to get the final sum.

Consider the set to be 1,2,3,4

${(\underset{}{鈭�} x_{i})}^{2} = {(1 + 2 + 3 + 4)}^{2} {(\underset{}{鈭�} x_{i})}^{2} = {(10)}^{2} {(\underset{}{鈭�} x_{i})}^{2} = 100$

and

$\underset{}{鈭�} {x^{2}}_{i} = 1^{2} + 2^{2} + 3^{3} + 4^{2} \underset{}{鈭�} {x^{2}}_{i} = 1 + 4 + 9 + 16 \underset{}{鈭�} {x^{2}}_{i} = 30$

As, resultrole="math" localid="1652990753066" ${(\underset{}{鈭�} x_{i})}^{2} 鈮� \underset{}{鈭�} {x_{i}}^{2}$

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91影视

Explain the difference between the quantities ${(\underset{}{鈭�} x_{i})}^{2}$ and $\underset{}{鈭�} {x^{2}}_{i}$ Construct 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 ∑xi2 and ∑x2i also construct an example to show that those two quantities are unequal

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91影视

Explain the difference between the quantities 鈭�xi2and 鈭�x2iConstruct 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 ∑xi2 and ∑x2i also construct 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

Statistics

Calculus

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Explain the difference between the quantities ${(\underset{}{鈭�} x_{i})}^{2}$ and $\underset{}{鈭�} {x^{2}}_{i}$ Construct an example to show that in general those two quantities are unequal.