_

sample mean x

^__    Σ x_{i    <---- sum of the values of the n observations}

X = _______

n    <---- number of observations in sample

(sample size)

approximate class width

equation

largest data value - smallest data value

number of classes

categorical or qualitative

data

• labels or names to identify attributes
• nominal or ordinal scale
• numeric or nonnumeric
• limited statistical analyses

i = (p / 100) * n

• if i is not an integer, round up; the pth percentile is the value in the ith position
• if i is an integer, the pth percentile is the average of the values in positions i and i + 1

• how much: real value may fall between intervals of scale
• the characteristic in reality can take on an infinite number or possible values

ex: height, weight, temperature, energy

• data collected at same or approximately same point in time

ex: take temp at 15 diff locations in rooom at beginning of class

the facts and figures collected, summarized,

     analyzed, and interpreted

the data collected in a particular study

the total # of data values in a complete data set

= # of elements * # of variables

tabular, graphical, and numerical methods

used to summarize and present data

• how many: counting whole things
• the characteristic in reality only takes on specific (integer) values

ex: people, votes, cars, lightning strikes, hurricanes

• a tabular summary of data showing the frequency(#) of items in each of several non-overlapping classes
• objective: to provide insights about data that can't be quickly obtained by looking only at the original data

• the data have properties of ordinal data, and interval between observations is expressed in terms of a fixed unit of measure
• always numeric
• zero point is arbitrary

ex: temperature (zero point doesn't mean no temperature)

mean

of a data set

the average of all the data values

• order of data has no particular meaning
• data are labels or names used to identify an attribute of the element
• a nonnumeric label or numeric code may be used

the set of measurements collected for a particular element

a data set with n elements has n observations

• the data have the properties of nominal data and the order or rank of the data is meaningful
• sorting provides additional meaning between one element and another
• a nonnumeric label or numeric code may be used

percent frequency

of a class

a sample statistic corresponding to a

population parameter  

the sample mean x is the point estimator of the population mean m

the set of all elements of interest

in a particular study

S x_{i        <----- sum of the values of the N observations}

_{m = --------}

N        <----- number of observations in population

• always numeric
• discrete (for how many)
• continuous (for how much)
• ordinary arithmetic operations make sense

• all properties of interval data and the ratio of two values is meaningful
• must contain a zero value that indicates that nothing exists for the variable at the zero point (absolute zero)

ex: distance, height, weight, time

relative frequency

of a class

scales of measurement

identify 4 types

• determines the amount of information contained in the data
• indicates the data summarization and statistical analyses that are most appropriate
• 4 types: nominal, ordinal, interval, ratio

• data collected over several time periods

ex: take temp at 15 diff locations at beginning, halfway, and end of class

• a measure of variability that utilizes all the data
• based on difference between the value of each observation (x_i) and the mean

for a sample

   S (x_i - sample mean)²

s^{2=-----------------------------------}

n - 1

for a population (census)

S (x_i - m)²

s^{2 = ---------------------}

N

mean: balance point of values

median: halfway point of the number of samples

mode: most "popular" value

z-score

equation

x_i - sample mean

z_{i  = -------------------------------------------}

s (standard deviation)