1) Sample Mean,

Average of the observations

Uses the magnitude of all the numbers

2) Sample Median, M

Order the observations

Median is the midpoint or average of middle pair

Want half below and half above

Represents a typical value

3) Sample Mode

Count up number of times each value occurs

Mode=most common (most frequent) value

Can be more than one

Example Average Stockton max temperature each month (1948-98)

(www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?castoc)

53 61 66 73 81 88 94 93 88 79 64 54

Example A study in Switzerland examined the number of hysterectomies performed in a year by doctors. A sample of 15 doctors gave: 27, 50, 33, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28

How many of the Swiss doctors were above the mean?

How many above the median?

The median is less affected by the extreme value = "resistant"

typical vs. total number

symmetric vs. skewed

Variability - How spread out are the values?

1) Range = Max-min

2) Deviations from mean

Average absolute difference of observations from mean

Average squared deviations from mean

4) Percentiles

Label the set of n observations:

To calculate the variance

The standard deviation is the square root of the variance