Math Problem Statement

SS Total ​ =195.7798− 15 (53.98) 2

Solution

To solve for the Total Sum of Squares (SS Total), we can use the formula provided. Based on the expression:

SSTotal=195.7798(53.98)215SS_{\text{Total}} = 195.7798 - \frac{(53.98)^2}{15}

Let's break it down step-by-step:

  1. Calculate (53.98)2(53.98)^2: (53.98)2=2916.8804(53.98)^2 = 2916.8804

  2. Divide 2916.88042916.8804 by 1515: 2916.880415=194.4587\frac{2916.8804}{15} = 194.4587

  3. Subtract from 195.7798195.7798: SSTotal=195.7798194.4587=1.3211SS_{\text{Total}} = 195.7798 - 194.4587 = 1.3211

So, the Total Sum of Squares, SSTotalSS_{\text{Total}}, is approximately 1.3211.

Would you like a further breakdown or additional help with related concepts?

Here are some related questions to explore:

  1. What does the Total Sum of Squares (SS Total) represent in statistics?
  2. How does SS Total relate to SS Between and SS Within in ANOVA?
  3. How would this calculation change if the sample size was different?
  4. What are the practical applications of calculating the Sum of Squares?
  5. How can this be used to find variance and standard deviation?

Tip: In ANOVA, breaking down the Total Sum of Squares into components like SS Between and SS Within can help explain the variation between and within groups.

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Math Problem Analysis

Mathematical Concepts

Statistics
Sum of Squares
Basic Algebra

Formulas

SS_{Total} = Total Sum - (Sum of Observations)^2 / n

Theorems

Properties of Sum of Squares

Suitable Grade Level

Undergraduate