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# Standard deviation

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1. Need some help with this one: ''let's say that the standard deviation for the body height among female adult swedes is 6 cm. What does that mean - explain!''

I do know what standard deviation is, I'm just not sure how to explain the example...
2. (Original post by Muminmamman)
Need some help with this one: ''let's say that the standard deviation for the body height among female adult swedes is 6 cm. What does that mean - explain!''

I do know what standard deviation is, I'm just not sure how to explain the example...
Basically how far each data point varies from the mean.

3. (Original post by RDKGames)
Basically how far each data point varies from the mean.

But is that it? I need an example of how I can answer to really understand the question. And like I said, I do know what the standard deviation is but what does a standard deviation of 6 cm tell us? Someone said the answer should include 68 %....
4. (Original post by Muminmamman)
But is that it? I need an example of how I can answer to really understand the question. And like I said, I do know what the standard deviation is but what does a standard deviation of 6 cm tell us? Someone said the answer should include 68 %....
It shows how spread the data is. A small s.d. means a lot of data is very close together.
5. (Original post by RDKGames)
It shows how spread the data is. A small s.d. means a lot of data is very close together.
Thank you so much! But what defines a small standard deviation? How do we know if it's small or large? I don't know if the picture is too small but can we say anything about if the 6 cm is within 68 %, 95 %...?

6. (Original post by Muminmamman)
Thank you so much! But what defines a small standard deviation? How do we know if it's small or large? I don't know if the picture is too small but can we say anything about if the 6 cm is within 68 %, 95 %...?

The 6cm is just the standard deviation. Assuming the the body height of adult female Swedes is normally distributed amongst a population, then you can say that 68.2% of the population lies within a single standard deviation away from the mean. If you were to go up to 2 standard deviations away from the mean, you would get 95.4% of the population, and so on. This is what the diagram there indicates.

You would have to know the mean and pick a height to see in what proportion of the population that value lies within. I.e. if and you pick a height which is as an example, you can work out that and this means that value is within the 95.4% of the population as it is more than 1 but less than 2 standard deviations away from the mean. In fact you can say that it lies between 68.2% and 95.4% of the population.

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