Standard deviation

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    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...
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    (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/sta...dard-deviation
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    (Original post by RDKGames)
    Basically how far each data point varies from the mean.

    https://www.khanacademy.org/math/sta...dard-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 %....
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    (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.
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    (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 %...?

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    (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 %...?

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    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.
 
 
 
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