Descriptive Statistics

what is a sample size

The number of samples or measurements that you take

what is sample size represented by

n

what is descriptive statistics

a mathematical way to describe your data

what two numbers can you use to describe your entire data set

central tendency and measure of variability

what is central tendency

where the peak of your data lies on a distribution curve

what is the measure of variability

the width of the distribution

wha are the three ways to describe the centermost point of a data set

mean, median, and mode

what is the mean

the average of all the numbers

what is the symbol for mean

x

when is it appropriate to use the mean

when the data set is parametric

what does parametric mean

it can be graphed into a perfect bell curve

what is another name for perfect bell curve

gaussian distribution

how do we find the mean

add up all the numbers and divide by n-1

what does the symbol E mean

sum

what does xi refer to

each individual measurement

what is the mean formula

X= E xi/n

what is the median

the middlemost measurement when arranged from least to greatest in a odd number of measurements data set

if the data set has an an even number of measurements what do you do

take the average of the two middle numbers

what is the mode

the most frequently occurring numbers

what are the symbols for standard deviation

S, O, or SD

what is standard deviation

describes the variability of individual measurements around the mean

how do we find the deviation of a measurement

it’s distance from the mean

the equation averages

the difference between each measurement (xi) and the mean (x)

what is the first step for standard deviation

take the mean

what is the second step of standard deviation

subtracting the mean from each measurement

what is step three of finding standard deviation

square all the deviances to correct outliers

what is step four for standard deviation

add up all the deviances

what is step five for standard deviation

divide by n-1

what is it called when n-1 is used

sample standard deviation

when is sample standard deviation appropriate to use

when you are sampling

if you can capture all members of the population what do you do instead

divide by n

what is it called when you just divide by n

population standard deviation

what is step six of standard deviation

take the square root

what do we use for popular standard deviation

greek lowercase s (o)

what should your standard deviation answer always have

+ and -

what should the range within one standard deviation be

68%

what should the range for two standard deviation be

95%

what is standard error

tells you how reliable the mean is and if it accurately represents a population

what is standard error most frequently called

standard error of the mean

what does standard error allow you to do

compare your mean to other means collected from the same population

how do you find standard error

divide your sample standard deviation by the square root of n

what does standard error depend on

n

the larger the sample size the

smaller the standard error

the smaller the standard error

more reliable the mean is

what does a large sample size mean

the more reliable the mean is

standard error represents

all possible means for a population

what do we use when we want to compare data from two different data sets

95% confidence interval

what is the 95% confidence interval

a range where the actual population mean is likely to fall

what is the range of values called

confidence interval

when comparing two data sets the confidence intervals either

overlap or don’t overlap at all

what does it mean if the confidence intervals don’t overlap

there is a significant difference between the two data sets

what does it mean if the internals overlap

we can’t be to sure so we say results are inconclusive and more tests are needed

what can be found in the intestinal tract of animals and the environment

ecoli

what are the two types of strains of bacteria

pathogenic and non-pathogenic

non parametric data can be

skewed or have multiple peaks

when is the mean appropriate

when the data set is parametric

when is median appropriate

when the data is non parametric and skewed

when is mode appropriate

when the data is non parametric and has multiple peaks

when is standard deviation appropriate

when the data set is parametric

what does deviation help determine

variability within the data set

what does standard error tell us

how reliable the mean is