Standard deviation
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Standard deviation is just a method of determining how closely data is centered around the average. The smaller the standard deviation, the repeatable and precise the measurement.
Let’s look at these three sets of numbers:
A – [5, 5, 5, 5, 5, 5, 5, 5, 5]
B – [1, 2, 3, 4, 5, 6, 7, 8, 9]
C – [0, 0, 1, 1, 5, 9, 9, 10, 10]
The average for all three of these sets is 5.
But the standard deviation for A is 0, the standard deviation for B is about 2.5, and the standard deviation for C is about 4.3.
The higher the standard deviation, the further spread out the numbers in the set are from the average.
“Deviation” comes from the word “deviate”, which means to go away from, and “standard” just means it is the standard way to measure it. “Standard deviation” is the standard way to measure how far away a set of numbers are from the set’s average.
Imagine you are a professor, standing in front of a large lecture hall partially filled with students.
Each student is a different distance away from you.
The *average* distance away from you is simply the total distance between you and each student added together and divided by the number of students.
But the average distance doesn’t tell you much about the spread of students in the room. For example, if there were 4 students, the average distance would be the same if those students were each sitting in one corner of the room or each sitting next to each other in the centre of the room.
The *standard deviation* tells you the average distance of each student *from the average distance between you and the students*. If that number is small, the students are close to each other, like the 4 students in the centre of the room. If it is large, they are far apart, like the 4 students in the corner.
Think about these two statements:
1. The average human has approximately two legs.
2. The average human is approximately 30.
Clearly, the first statement describes the average human much better, this is because the standard deviation of the distribution of the number of legs is extremely small. That is, the average is 2 because pretty much everybody has 2 legs, except some very small portion of the population.
The second statement is a bit silly, sure, the average age on Earth is about 30, but if you walk down the street you’ll see people of all different ages, and knowing the average by itself doesn’t tell you much about the population. This distribution has a much higher standard deviation.
Standard deviation measures how far from the average the actual numbers in a distribution are, on average. It’s literally the average of the squared difference of a random variable and its average.
Group A: One rich kid and one poor kid. Rich kid income is $3990, poor kid income is $10. Average income of group A is $2000
Group B: 2 middle class kids. Both kids income is $2000. Average income of group B is $2000
Both groups have the same average of income but group A has larger deviation. It means the member of the group has more ‘difference’.
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