As announced earlier, we will be picking up from the past blogs and translating it into English from today. It is poor English, but please forgive. You may not understand a part sometimes.
If you want to understand statistics in the future, understand these two items: One is to imagine "Dispersion." Second, understand how to quantify "Dispersion."
See documentation. → Dispersion(2018.11.7)
p.1: Explain using a balance with a suspended weight. Calculate the distance from the "center of gravity" where you can balance. Add a minus to the distance to the left-side weight. For balances A and B, calculate the sum and average of the distances. Each average is zero. As a result, the average value cannot be used as an indicator of “Dispersion”.
p.2: Calculates the sum and average of the squares of the distances. The value of A is 7.5 and B is 2.5. The value of A with a large "Dispersion" is a large number. "Dispersion" could be quantified.
p.3: Consider whether the average of the absolute value of the distances from the center of gravity indicates " Dispersion ". This value is the "Manhattan distance" from the previous blog.
p.4: For B and C balances, use the distance from the center of gravity to the weight as the absolute value, calculate the sum, and calculate the average. Both values of B and C have the same value. Absolute values cannot be used as an indicator of " Dispersion ".
p.5: In the case of C, the average of the sum of squares of the distance is 3.0. This indicates that A's Dispersion is slightly greater than B's one. Within the balance of A, B, and C, the average of sum of squares is greater for Balance A, indicating that the " Dispersion " is the largest. This " Dispersion " is called "Variance" in statistical terms and the symbol is V. "Standard deviation σ" is the square root of "Variance V", and the order of " Variance " is not changed. Why do we need to calculate the square root of V? This means returning to dimension of units. Please see the next page.
p.6: This graph shows a normal distribution with an average body weight of 60 kg and a standard deviation of σ: 10kg. The inflection point is the standard deviation σ. If you leave "Variance V" alone, it will be 100 kg2, making it difficult to draw graphs. So use square root to go back to the original data unit kg