Statistics 简明教程
Statistics - Sum of Square
在统计数据分析中，总平方和 (TSS 或 SST) 是一个作为此类分析结果中标准方式一部分出现的量。它被定义为所有观察值的总体平均值的每个观察值的平方差之和。
In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. It is defined as being the sum, over all observations, of the squared differences of each observation from the overall mean.
总平方和由以下函数定义和给出：
Total Sum of Squares is defined and given by the following function:
Formula
其中——
Where −
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${x_i}$ = frequency.
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${\bar x}$ = mean.
Example
Problem Statement:
Problem Statement:
计算身高分别为 100、100、102、98、77、99、70、105、98，平均值为 94.3 的 9 个儿童的平方和。
Calculate the sum of square of 9 children whose heights are 100,100,102,98,77,99,70,105,98 and whose means is 94.3.
Solution:
Solution:
给定的平均值 = 94.3。求平方和：
Given mean = 94.3. To find Sum of Squares:
Calculation of Sum of Squares. |
Column A Value or Score ${x_i}$ |
Column B Deviation Score ${\sum(x_i - \bar x)}$ |
Column C ${(Deviation\ Score)^2}$ ${\sum(x_i - \bar x)^2}$ |
100 |
100-94.3 = 5.7 |
(5.7)2 = 32.49 |
100 |
100-94.3 = 5.7 |
(5.7)2 = 32.49 |
102 |
102-94.3 = 7.7 |
(7.7)2 = 59.29 |
98 |
98-94.3 = 3.7 |
(3.7)2 = 13.69 |
77 |
77-94.3 = -17.3 |
(-17.3)2 = 299.29 |
99 |
99-94.3 = 4.7 |
(4.7)2 = 22.09 |
70 |
70-94.3 = -24.3 |
(-24.3)2 = 590.49 |
105 |
105-94.3 = 10.7 |
(10.7)2 = 114.49 |
98 |
98-94.3 = 3.7 |
(3.7)2 = 3.69 |
${\sum x_i = 849}$ |
${\sum(x_i - \bar x)}$ |
${\sum(x_i - \bar x)^2}$ |
First Moment |
Sum of Squares |