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### Course: Statistics and probability>Unit 3

Lesson 4: Variance and standard deviation of a population

# Population standard deviation

The population standard deviation is a measure of how much variation there is among individual data points in a population. It's a way of quantifying how spread out the data is from its mean. A small standard deviation means that the data points are generally close to the mean, while a large standard deviation means that the data is more dispersed. Created by Sal Khan.

## Want to join the conversation?

• Isn't the dividing part wrong?
I learned it should not be 5 in this case, but it should be 4 which is n-1.
• You divide by "n-1" when dealing with the Sample Standard deviation. In this video Sal is calculating the Standard deviation of the population, which is why he is dividing by "N".
• How could the concept of variance be usefull in real life ?
• So in this example the standard deviation is 0.562 meters, does that mean that the 5.5 meters of the original data set is a bit of an outlier since it's not within the standard deviation of the mean?
• What does Population standard deviation mean??
• The standard deviation of the population. Most if not all the values that we quantify in the field of Statistics - things like the mean (average), or median, or standard deviation, etc - can be thought of in two ways:

1. What is the value of the quantity considering only our sample data? This is what we call a "statistic".

2. What would be the value of the quantity if we were able to get data on the wheel population, meaning every possible data point. This is what we call a "parameter".

So there are statistics and parameters. We use a statistic to estimate (make an educated guess at the value) of a parameter. The population standard deviation is simply referencing the population parameter, rather than the sample statistic. Sometimes (often) the value of the parameter is unknown or even unknowable, but we can still think of it in theory.
• Sal's question makes sense, why don't take the absolute value of it instead of take it to second power?
• Is 'var' the short form of variance?
• It depends on the context, I've seen it used for both. If it seems to be representing a single number or a function, then it's probably variance. If it seems to reference several characteristics (e.g. height, weight, eye color, etc), then it probably means variables.
• so both Variance and standard deviation are used to measure level of dispersion. what's the difference when you need to pick one to solve real-world problem?
• It's true that they both are used to measure the level of dispersion but the difference is that the SD is a "true" average distance from the mean. Therefore, SD is more "useful." Variance is just a step before you get SD.
• with n=13 and p=0.5 find p( at least 10)
• you said that p= 0.5 so the anser is 0.5
(1 vote)
• At when I used my calculator I got a different answer it said 18.6 instead of 4.6 I am quite puzzled because I have repeated the calculation correctly and still I have the same wrong answer 18.6.
(1 vote)
• Are you sure you've input the decimals properly? The answer is 4.6. The numbers are 4.0, 4.2, 5.0, 4.3 and 5.5.