mean
measure of center found by adding the data values and dividing the total by the number of data values
- the mean is relatively reliable and more relieable than other measures of central tendency
-it takes every data value into account
-just one extreme va
median
the middle value of a set of numbers
-
mode
-occurs with the greatest frequency
-data set can have one mode, or no mode
-bimodal- when two data values occur with the same greatest frequency
bimodal
when two data values occur with the same greatest frequency
multimodal
when more than two data values occur with the same greatest frequency each is a mode and that set is said to be multimodal
no mode
no data value is repeated
midrange
uses only the maximum and minimum values.
-rarely used because is too sensitive to those values
= max data value+min data value/2
round off rule for mean median and midrange
carry one decimal place more than is present in the original set of values.
mean from a frequncy distribution
...
weighted mean
...
skewed
the distribution is not symmetric and extends more to one side than to the other.
symmetric
the left half of the histgram is roughly a mirror image of its right side
negatively skewed
skewed to the left
-has a longer left tail and the mean and median are to the left of the mode
positively skewed
has a longer right tail
-the mean and median are to the right of the mode
trimmed mean
with data in order, take off the top 10% of the values and bottem 10% of the values to get the 10% trimmed mean
harmonic mean
used with data sets with rates of changing calues such as speed.
-found by dividing the number of values by the sum of the reciprocals of all values.
- expressed as:
geometric mean
used in business and economics for finding average rates of change, growth and ratios.
quadratic mean
also known as root mean square
-used in physical applications.
-
range
the difference between the maiximum data value and the minimum data value
-very sensitive to extreme values
-used ub statistical process control because it is so easy to compute
standard deviation
a set of sample values denoted by s
-a variation of values about the mean
-a type of average deviation of values from the mean that is calculated by using this formunla-
variance
the square of the standard deviation