Mod. 1 Ch. 3 - Means and Standard Deviation

the 68-95-99.7% rule applies for

roughly all bell-shaped curves

Range is the

difference between the largest data value and the smallest

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

mode can be used for both

quantitative and qualitative

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