# Standard Deviation

Hi there,

I am working through the start the data analytics course and could use a little help on the standard deviation questions.

In this project I am provided a mean of 6.3 and a standard deviation of 1. I’m not quite following how they determined that "most scores fall between 4 and 8 " on the attached graph.

Can someone help this make sense to me?

It’s a bell curve distribution. You’re looking at the spread of the data. If the SD is low, then it translates that most of the scores/values fall close to the mean of 6.3, or within 1. SD is how much variation there is in the data. If you look at the data points, most do fall within 4 & 8.

To calculate the SD, you would take each data point and subtract it from the mean, then square it. (ex: (4.5-6.3) squared= 3.24, etc. etc. Then add up all data points and divide by the number of points to get the variance (how the data is spread out), the standard deviation is equal to the square root of the variance, or 1.

About 95% of the values in a normal distribution can be expected to lie within two standard deviations of the mean.

Mean is 6.3, s.d. is 1, so about 95% of values can be expected between 4.3 (≈ 4) and 8.3 (≈ 8)