Standardising data and normal distribution - L5

What does standard deviation measure?

The average deviation of all values from the mean

How is standard deviation displayed?

In brackets after the mean

What should you do if the true value of a piece of data is unknown?

Record a missing value

What are the 2 ways to transform data?

• Scale the data

• Standardise the data

What is scaling the data?

Converting all of the data values into the same units

What is standardising the data used for?

To be able to compare different sexes or not directly comparable categories

What happens to the mean if data values are re-adjusted by adding or subtracting?

It increases or decreases by the value added or subtracted to each data value

When you multiply or divide to scale data, what happens to the mean and standard deviation?

They both increase or decrease by the proportion being multiplied or divided by

What does a z-score measure?

The number of standard deviations an observation is from the mean

What does a z-score of 0 indicate?

A value that is equal to the mean

How do you calculate a z-score?

(observation - mean)/standard deviation

What is the mean of all z-scores always equal to?

0

What is the standard deviation of all z-scores always equal to?

1

What are 6 properties of normal distribution?

• The curve is symmetrical about the mean

• The mean is equal to the median

• Most observations are closer to the mean

• Few observations are at either extreme

• Lines of the curve don’t touch the x-axis

• The shaded area under the curve always equals 1.0

What percentage of normally distributed data lien within ± 1 standard deviation of the mean?

68.2%

What percentage of normally distributed data lien within ± 2 standard deviations of the mean?

95.4%

In normal distribution, what is 1 z-score equal to?

34.1% or 0.341