Last lecture summary• Types of statistics• Measures of central tendency• Measures of variability

• Bias, Bessel's correction• MAD• Normal distribution• Empirical rule• Standard normal distribution, Z-distribution

Standard deviation – empirical rule

Standard deviation – empirical rule

Standard deviation – empirical rule

New stuff

Use Z-tableWhat proportion of people is smaller than 180 cm?

Z-value of 1.4 corresponds to 91.92%.

Quiz – height data

• What proportion of people is smaller than you?• see Z-table

• What proportion of people is taller than you?• see Z-table• Table gives a value “less than”.• Note, that “greater than x” is the same as “less than -x”.

Quiz – height data

• What proportion of people lie between you and you?

• How tall should you be to be in the top 5% of the highest people?

The nature of the normal distribution• In laboratory experiments, results vary due to several

factors: imprecise weighting of reagents, imprecise pipetting, nonhomogeneous suspensions of cells or membranes ...

• Similarly, variation in a clinical value might be caused by many genetic and environmental factors.

• These random factors are independent and they tend to offset each other.

• Variation among values will approximate a Gaussian distribution• when there are many independent sources of variation• when individual sources add up to get the final result

DISTRIBUTION, DISTRIBUTION, ARE YOU NORMAL?

http://www.nate-miller.org/blog/how-normal-is-normal-a-q-q-plot-approach

Life expectancy data – histogram

life expectancy

freq

uenc

y

Making conclusions from a histogram• What can you tell about life expectancy data?

• how many modes?• where is the mode?• symmetric, left skewed or right skewed?• outliers – yes or no?

life expectancy

freq

uenc

y

Making conclusions from a histogram• Where is the mode, the median, the mean?

life expectancy

freq

uenc

y

Min. Q1 Median Q3 Max. 47.79 64.67 73.24 76.65 83.39

Five numbers summary

8.5>3.5

25.4>10.2

mean=69.9