Reading Quiz 2 Flashcards
True or False: the standard score for any observation tells how many standard deviations that score is from the mean.
true
What two steps do we do to standardize a score?
subtract the mean and divide by the standard deviation
standard score is often called by what other term?
the z-score
What does the sign of a standard score correspond to?
its direction: if the z-score is positive it’s above the mean and if it’s negative it’s below the mean
The scales of density curves are adjusted so that the total area under each curve is what? A. 1
1
The area under the density curves between a couple of x-axis values represents what?
the proportion of all observations that fall between those values
Do measures of center and spread apply a to density curve as well as to sets of observations?
yes
How do you define the median of the density curve?
the point with half the area under the curve to its left and the remaining half of the area to its right
The quartiles of a density curve divide the area into what?
four equal parts
What is the relationship between the mean and the median of a symmetric density curve?
they are equal
Which is pulled the farther toward the tail of a skewed distribution: the median, or the mean?
the mean
In conventional notation, what are the meanings of x and s, as contrasted to and ?
the first two refer to the mean and standard deviation, respectively, of a set of observations, a sample. the second two refer to the mean and standard deviation, respectively, of a density curve idealized distribution, or the population distribution
What three features describe the overall shape of normal curve?
normal curves are symmetric, single peaked (unimodal), and bell shaped
Is there only one normal curve, or is there an infinite number of normal curves?
an infinite number
For any given mean and standard deviation, is there only one normal curve, or an infinite number of
normal curves?
only one
How can you visually find the points of one standard deviation from the mean of a normal curve?
those points are the inflection points of the curve. there, the curve changes from falling more and more steeply to falling less and less steeply, or vice versa.
The distributions of test scores, of measures of characteristics of living things, and of summary statistics for chance outcomes repeated many times, often (but not always!) follow what type of distribution?
normal distribution
What three percentages do you have to remember when you are stating the “empirical rule?”
A. 68%, and 95%, and 99.7%.
68%, 95%, 99.7%
Are the three percentages for 1, 2, and 3 standard deviations exact, or easier-to-remember rounded approximations?
approximations
What do the three percentages in the empirical rule apply to? In other words, what is the meaning of this rule?
the three numbers tell the percent of observations falling within the region plus or minus 1, 2, or 3 standard deviations from the mean, respectively, in a normal curve
True or false: If Mary scores one standard deviation above the mean on a normally distributed test, then approximately 68% of the test takers scored as close to the mean of the test as, or closer to the mean than, Mary did.
true
True or false: If Mary scores one standard deviation above the mean a on a normally distributed test, her score is in the 68th percentile.
false
True or False: if Mary scores one standard deviation above the mean on a normally distributed test, half of 68% or 34% are above the mean but at or below Mary’s score. An additional 50% are below the mean. Thus Mary equals or surpasses 50% plus 34% of the test takers, and is at the 84th percentile.
true
What does the notation N(100,15) mean?
it denotes a normal distribution with a mean of 100 and standard deviation 15
In a standard normal distribution, what is the value of the sample mean of the z-scores and the sample standard deviation of the z-scores?
sample mean 0
sample standard deviation 1
In a table of areas under the standard normal curve, what does the table entry for each z score represent?
the area under the curve to the left of z, or in other words, the proportion of cases with values less than z
What steps do you follow with a z table if you want to know what proportion of the scores are between two values?
look up the proportion less than the first, and less than the second, and find the difference between the two proportions
What steps do you follow with a z table if you want to know what proportion of the scores are greater than a value?
look up the proportion less than the value then do 1 minus that proportion
What do the authors recommend (as a word to the wise for future test-takers) as the last step of problems giving a normal distribution and asking for proportions of observations?`
they recommend stating the conclusion in the context of the problem. thus, rather than just saying the answer is 49%, you would say, “about 49% of boys have cholesterol levels between 170 and 240 mg/dl”
What steps do you go through when you want to find a value given a proportion of a normal distribution, using the z-table?
you look for the proportion in the body of the table, and you find at the margin the z-score that corresponds to it. then you unstandaqdize the z-score
What operations do you do, and in what order, to “unstandardize” a z-score, or turn the z-score into a raw score?
you multiply the z-score by the standard deviation then you add it to the mean
percentiles
measure location relative to median
z-scores
measure location relative to mean
what to do if you have duplicates
choose highest one
standardizing
converting raw data to standard deviation units
gives z-score, tells you how many standard deviations away from the mean the observation falls and in which direction
z-score formula
z = (observation - mean)/standard deviation
when is the median the highest point
only when the data is symmetric
what is the rule called
either 68-95-99.7 rule
or the empirical rule
rule
can only use with normal data
Density curve
Always lies on or above the horizontal axis
Has area exactly one underneath it
Approximates shape of actual distribution
Most commonly used family of density curves are normal curves
Median v mean in density curve
Median divides area under curve ni half
Mean is point at which curve would balance if it was made of solid material
Standard normal distribution
N(0, 1)
