what are descriptive statistics
statistics used by researchers to report on samples.
summarize information to speed up and simplify the comprehension of a population’s characteristics.
how do descriptive techniqes organize data
tables
 freq distributiona
 relative frequency distrubutiona
graphs
 bar chart
 histogram
 boxplot
how do descriptive stats summarize data
central tendency/ mid sample value (location)

Mean

Median

Mode
variation summary diff w/in a groupm(spread)

Range

Interquartile range

Variance

Standard deviation
what is the mean
average
add up values for each case and divide by total number of cases
describe the median
 The middle value when a variable’s values are ranked in order
 point that divides a distribution into two equal halves

if data are listed in order, point at which 50% of the cases are above and 50% below it

The 50th percentile
if data are listed in order, point at which 50% of the cases are above and 50% below it
The 50th percentile
describe the mode
 the most common data point
 if all values are unique then there isnt one
 is not always at the centre of distribution
 can be multiple
define the spread
the Variation of the recorded values on a variable
 larger spread has cases further from mean
 smaller spread has individual cases to the mean
describe the range
distance, between the lowest and highest values of a variable.
highest value lowest value.
describe Standard deviation
 how much the members of a group differ from the mean value for the group.
 larger deviation = increased variation from mean
 equal to 0, only when all values are the same ( constant and not a “variable”).
what happens to the mean When a constant is added to every observation
new sample mean is equal to original mean plus the constant.
what happens to the standard deviation when a constant is added to every observation,
standard deviation is unaffected.
what happens to the sample mean when every observation is multiplied by the same constant,
new sample mean is equal to original mean multiplied by the constant.
what happens to the standard deviation when every observation is multiplied by the same constant,
new sample standard deviation is equal to original standard deviation multiplied by the magnitude of the constant.
what is the normal distrubution
MEAN and SD are appropriate for histogram summary
bell shaped curve where the mean is at it's peak
histogram: graphical display of data using bars of different heights
what are the three rules of sigma when data has an approx normal distribution
approximately 68% of the data lie within one SD of
the mean
approximately 95% of the data lie within two SDs of
the mean
approximately 99.7% of the data lie within three SDs
of the mean
what is the difference betw/ standard error of a mean & standard deviation
when the mean estimates individual values standard deviation = the degree of uncertainty by which the mean estimates individual values
when the mean estimates the population mean standard error of mean = the degree of uncerntainty with which the mean estimates the population mean
what is the confidence interval of the mean
a range of values around the mean where we expect the "true" population mean is located.
µ=x+/1.96xSEM
example

X = 9.5 years; SD = 2.8 years
SEM = 0.5 years
95% level of confidence => Z = 1.96
µ = 9.5 ± (1.96 x 0.5) = 9.5 ± 1 years
95% CI for µ is (8.5; 10.5 years)