Statistics & Data Analysis Unit 4

If we multiply every value in a data set by a constant (a) what happens to the summary statistics?

Mean, median, quartiles, standard deviation, IRQ, range get multiplied.

Vice versa divided.

If we add a constant (b) to every value in a data set what happens to the sammary statistics?

Spread values (IRQ, standard deviation, range) do not get effected. They stay the same.

The mean, median, and quartiles get affected, the constant is added to them. 

Percentile

If an observation is in the pth percentile, it means that p% of the data is less than or equal to the observation.

How can we compare one observation to another observation if they dont have the same mean and std. dev?

You measure both observations in terms of their means & std. deviations- then we can compare them

Standardizing

• Gives the number of standard deviations an observation is away from its mean

• Called a Z-score or standing score

• Z= (observation-mean)/(std. dev)

• Gives direction: (+)=above mean, (-)= below mean

• It has no units

• Does not change- the shape of the distribution

• Changes the center by making the mean =0

• Changes the spread by make the std. deviation =1