Standard deviation

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...

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.

https://www.khanacademy.org/math/statistics-probability/displaying-describing-data/sample-standard-deviation/v/statistics-standard-deviation

(edited 7 years ago)

Reply 2

Muminmamman

OP

Original post by RDKGames

Basically how far each data point varies from the mean.

https://www.khanacademy.org/math/statistics-probability/displaying-describing-data/sample-standard-deviation/v/statistics-standard-deviation

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 %....

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.

Reply 4

Muminmamman

OP

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 %...?

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

\mu = 175

and you pick a height which is

184 \text{cm}

as an example, you can work out that

\frac{184-175}{6}=1.5

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.

(edited 7 years ago)

Standard deviation

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