Sum of squares (statistics)
Imagine you have five stickers, one is a flower, one is a star, one is a heart, one is a square, and one is a circle. Each sticker has a number on it - 3, 5, 6, 7, and 8.
Now, your friend came to you and asked you to find the total value of these stickers by adding up the number of each sticker. What you do is add them up and get the result - 3+5+6+7+8 = 29.
But, another friend comes and asks you something different. They want to know how spread out the numbers are on these stickers. This is where sum of squares comes in.
You take the difference between each sticker and the mean value (which is the sum of all sticker values divided by the number of stickers). So, you subtract 29/5 = 5.8 from each sticker value, getting you:
(3-5.8)^2 + (5-5.8)^2 + (6-5.8)^2 + (7-5.8)^2 + (8-5.8)^2
= 7.84 + 0.64 + 0.04 + 0.36 + 4.84
= 13.72
This is the sum of squares or the measure of how spread out the numbers are. A larger sum of squares means that the numbers are more spread out, while a smaller sum of squares means that the numbers are closer together.
Now, your friend came to you and asked you to find the total value of these stickers by adding up the number of each sticker. What you do is add them up and get the result - 3+5+6+7+8 = 29.
But, another friend comes and asks you something different. They want to know how spread out the numbers are on these stickers. This is where sum of squares comes in.
You take the difference between each sticker and the mean value (which is the sum of all sticker values divided by the number of stickers). So, you subtract 29/5 = 5.8 from each sticker value, getting you:
(3-5.8)^2 + (5-5.8)^2 + (6-5.8)^2 + (7-5.8)^2 + (8-5.8)^2
= 7.84 + 0.64 + 0.04 + 0.36 + 4.84
= 13.72
This is the sum of squares or the measure of how spread out the numbers are. A larger sum of squares means that the numbers are more spread out, while a smaller sum of squares means that the numbers are closer together.
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