ch 3 descriptive statistics: probability and meas of central tendency Flashcards
central tendency
• Central tendency indicates the centre of the data and is dependent on the analysis technique used
how do you define th central tendency of a distribution
depends on alaysis techniques used which in turn depends on the level of meas of the data
____ variables are for categorical differences like gender.
nominal
what is the ONLY meas of central tendency for nominal data
mode
when applying mode to nominal variable is it possible to have multiple modes or two modes
• can have two modes (bimodal) or be multimodal
what level of meas is necessary for calculation of median
data must be rank ordered (ordinal, interval or ratio)
what level of meas is necessary for calculation of mean
ONLY if avail data is at interval or ratio leve
what is range
• range is difference between max value and min value of a variable
which is frequently better meas of central tendency for interval or ratio level data
median or mean
median
why is median frequently better meas of central tendency for interval or ratio level data
outliers can distort the data when using mean
standard deviation
• standard deviation is avg distance the values fall from the mean.
when you have a large Std deviation does t mean there s a small or big spred in values in the data
Lg SD=lg spread
when spread is small most of the avg scores are close to avg score
what is inferential statistics
involves associating probabilities with each variable studied
what is probability
• Probability is the chance that a particular outcome will occur
not sure why they go on abt not being able to say that probabiity is 100% and instead the researcher must say….
the probability approaches 100%?
same thing applies to 0% “the probability approaches 0”
what is frequency distribution
lists all possible outome of an experiement and tallies the number of times each outcome occurs. this is then graphed to make easier to understand and see
what is probability distribution
• Probability distributon graphs probability of all possible outcomes of the variable rather than their frequency. Eg when rolling dice the probability distribution never changes but the frequency distribution changes depending on the sample
if you are rolling dice x1000 and made a frequency distribution of how frequently you roll each number how would it compare to the probabiity distribution of rolling a die indefinitely
when rolling dice the probability distribution never changes but the frequency distribution changes depending on the sample
what shape does a normal distribuion have
bell curve
in a normal distribution where o you find the mean median and mode
is a normal distribution a type of probability distribution
• Normal distribution ( bell curve) has a probability distribution where the mean median and mode are the same
yes it is
o In normal distribution you know __ of its values fall within 1 SD of the mean
68%
in normal distribution you know ___ of its values fall within 2 SD of the mean
95%
what type of distribution is enerally seen as the most important kind in stats?
normal
what are the 2 facts abt normal distrib that make it so important
1-if you take the mean from lots and lots of samples of a pop the distribution of the sample means (the sampling distrib of the mean) becomes normal in the long run. SAMPLING DISTRIBUTIONs plots actual frequencies of a stat vs the range of possible values that statistics can take
2-as you add more and more random variables toether their overall distrib approaches the normal distrib
for normal distribtuion Increasing the mean moves the curve shift to the ____ and dec it makes it move ___
o Increasing the mean moves the curve shift to the right and dec it makes it move left
if normal distribution what does it do to the shape when you dec the variance? or inc it?
o Dec the variance makes the graph taller and skinnier and inc makes it shorter and fatter
t or f any normal variables distribution can be transformed into std normal distribution
true
how does a skewed distirbution occur and what is it
• Skewed distribution is an assymeterical distrib of the values of the variable around the mean, making one tail longer than the other
o Skewing isusually d/t lg number of outliers.
skewed distribution when outliers are on the right the skew is ____? what about on left?
When outliers are on right then the skew is positive. If on the left its negative
t or f
with skewed distribution the mean, median and mode arent the same
o When skewed the mean median and mode aren’t equal
what can you use on normally distrib data to see how many standard deviations the observation is from the mean
z score
what is a z score
It is a standardized meas that tells you how many SDs the observation is from the mean
you have a positive z score what does this mean
o If the value is above the mean or avg itll have a positive z score
o The larger the absolute value of the z score the _____ the value is from the avg or mean value in the data set
further
what are z scores helpful for
-can be helpful since we know assoc probability 95% of the values fall between 2 std deviations or z scores of approximately -2 to 2+
comparing different data sets eg you get a score of someones ROM exercise (17 and then your z score is -0.5 which would mean their score is worse than avg)
so basically the absolute value of that score doesnt tell us the relationship of the score to the other outcomes/scores
how do z scores relate to standard deviation
a z score of 2.0 lies 2.0 std deviations above the mean. While a z score of -0.5 lies 0.5 std deviations below he mean
what kind of data can median be used with (level of meas)
ordinal, interval, ratio
what two concepts are important in relation to the dispersion of your data
the range
the standard deviation
