Mod. 1 Ch. 3 - Means and Standard Deviation
the 68-95-99.7% rule applies for
roughly all bell-shaped curves
How to find mean in odd N or n
find the middle value
Population arithmetic mean, and it's symbol
mean computed by using all individuals in a population, symbol is "mew"
Sample arithmetic mean
mean using sample data, symbol is "x-bar"
inter-quartile range contains the
middle 50% of all observatoins
Population mean is a
parameter
When finding the mean of a set of data you should always do what first
put data in order!!!! median will be skewed otherwise
Mode is primarily a measure of
qualitative central tendency
The sum of the deviations about the mean always equals
0 because observations greater than the mean will offset the observations less than the mean and cancel out to zero or close to zero
95% of values in a normal distribution fall within
2 Standard deviations [95-68= 27/2 = 13.5] >> (13.5% | 34% () 34%|13.5%)
Inter-quartile range
Q3 minus Q1
Resistant means
is the measure of central tendencies resitant to extreme values, does it alter the data significantly
N means
population
"Mu" [µ] means
population mean
How to find mean in even N or n
take the mean of the middle 2 values
Percentile
the Kth percentile, denoted Pk of a set of data is a value such that K percent of the observations are less than or equal to the value represented by the percentile, like class rank but the percentil starts from low to high, so 5th percentile is 5% of population has this or less and so forth, 95th is the top 95% of the data, and 95% of individuals and this number or less
Standard deviation allows you
to see how spread out or concentrated the data in a bell curve is, should be able to pic which graphs go with which µ and "x-bar" and σ
[St.Dev. 1]+[St.Dv. 2] = [34.7 + 13.5] = 48.2% probability
What is the probability that a randomly selected time falls between 40 and 42 seconds?
(Σxi)/N means
sum of all x values / N - population
Mode
variable that is most the most freequent observation, N or n's can be no mode, single mode, bimodal or multimodal
Σxi
{sum of}{all x values}
Varience is
(standard deviation)^2
99.7% within 3 Standard deviation
[99.7-95= 4.7/2 = 2.35% >> [2.35% |..|.. () ..|..|2.35%]
Arithmetic mean
adding all values of variables and dividing by number of variables
Σ is called and means
Uppercase sigma, and means the "sum of terms [xi]"
n means
sample
which measures of central tendencies are not resistent
mean, range and standard deviation
the higher the standard deviation
the more spaced out and dispersed the bell shape.
Median is, symbol is
value that lies in the middle of the data when arranged in ascending order. M is the symble
The standard deviation is used in conjunction with the _____ to numerically describe distributions that are bell shaped. The ____ measures the center of the distribution, while the standard deviation measures the ____ of the distribution.
The standard deviation is used in conjunction with the MEAN to numerically describe distributions that are bell shaped. The MEAN measures the center of the distribution, while the standard deviation measures the SPREAD of the distribution.
xi means
all x values
Why is range not a good measure?
because it doesn't give you how wide the data is talking about but not weather it's scrunched or dispersed or how many n or N is
Which measures of central tendencies are resistant
median and mode
True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.
True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
"x-bar" means
sample mean
which percent of observations are expected to lie within 1 standard deviation of the mean?
68% >> (34% () 34%)
Emperical rule is known as
68%-95%-99.7% rule
Range is the
difference between the largest data value and the smallest
mode can be used for both
quantitative and qualitative