Question

Explain how the scattering of raw scores throughout a distribution would

affect the standard deviation. That is, how would the standard deviation be affected if

the data points were very tightly clustered versus if they were quite spread out?

Answer 1

Standard deviation measures the spread of data values in a distribution. It is measured using the deviation of each data value from the mean. The standard deviation increases, if data values have higher deviation, which means, the more scattered data values are, the higher standard deviation it will have.

If the data points were very tightly clustered, the standard deviation will be very low. If all points are the same, that is there is no deviation from the mean, the standard deviation is 0.