Task 2 Flashcards
Statistics are also known as…
estimates
What do density curves represent?
the probability of a continuous random variable
Density curves are used on
histograms
What is the area under a density curve?
1
What kind of density curves are there?
normal, symmetric, skewed etc
Where is the mode on a density curve?
the highest point
How do you calculate the median on a density curve?
total area halved on each side
How do you locate quartiles on a density curve?
divide the area into quartiles
The larger the standard deviation, the larger the…
spread
Percentages for normal distribution
68% 95% 99.7%
Define standardizing
a linear transformation that transforms data into the standard scale of z-scores
What does a z score tell us?
tells us how many standard deviations the original observations fall away from the mean and in which direction
If observations are larger than the mean they are
a) positive
b) negative
when standardized
positive
Does standardizing affect the distributional characteristics e.g. shape and cumulative density?
no
What is the mean of the standard normal distribution?
0
What is the standard deviation of the standard normal distribution?
1
Define cumulative proportion
the proportion of observations a distribution that lie at or below a given value
Does standardizing changes the slope and intercept of the line in our plot?
yes but the line does not turn
How do we find the sampling distribution of the mean of x?
we take as many simple random samples of size 80 and calculate the mean for each sample
What does the precision of an estimate depend on?
the spread of the sampling distribution
What is the Central Limit Theorem?
draw a SRS of size n from any population with population mean and finite standard deviation
when n is large, the sampling distribution of the sample mean is approx normal
Define exponential distribution
a process in which events occur continuously and independently at a constant average rate
What does the mean and standard deviation equal in an exponential distribution?
1
What is the formula to calculate the height under a density curve at a given point x?
see notes page 2
Define unbiased estimate
applies to sample mean, expected value of sampling distribution of the statistic of interest = parameter of interest in the population
i.e. μx̅ = μ
Define efficiency
an estimator is more “efficient” than another if the spread is smaller
Efficiency is in relation to a ____ and variability is in relation to a ____
statistic, variable
Define standard error
a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates (related to sampling distribution)
Define central limit theorm
in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
What kind of variables are estimates?
random variables
A sample is an example of a ___ ____
elementary outcome
What kind of distribution is a sampling distribution?
a theoretical distribution
What makes an estimate unbiased?
if averaged across an infinite number of estimations it would yield the parameter again
Why is the standard deviation of a sampling distribution also known as the standard errror?
Because its the average deviations a mean will deviate from the actual mean when various samples are drawn
How can we minimise the standard error?
drawing a larger sample e.g. larger than 25
How can we make x bar a more efficient estimator?
increase sample size as it reduces standard error therefore predicts the population much better
What do disjoint events look like on a contingency table?
=0
Are distribution and bias related?
no
What do outliers do to the mean?
skew it
Always draw with replacement unless ….
conditional
What distribution represents population distribution better?
a) sampling
b) sample scores
b
