Chapter 1

statistics

the science and act of collecting, analyzing and drawing conclusions from data

individual

is an object described in a set of data. Individuals can be people, animals, or things.

variable

an attribute that can take different values for different individuals

categorical variable

assigns labels that place each individual into a particular group. called a category.

quantitative variable

takes number values that are quantities-counts or measurements.

discrete variable

a quantitative variable that takes a fixed set of possible values with gaps between them. (for example, a gymnastic score given on a scale of 1-10 which is almost always a decimal)

continuous variable

a quantitative variable that can take on any value in an interval on the number line. (time, height, things that can be real numbers (so not negative)).

distribution

of a variable tell us what values the variable takes and how often it takes those values.

dot plot

shows each data value as a dot above its location on a number line.

symmetric

if the right side of the graph ( containing the half of observation with the largest values) is approximately a mirror image of the left side.

skewed right

if the right side of the graph is much longer than the left side. mean is greater than median.

skewed left

the left side of the graph is much longer than the right side. Median is greater than the mean.

SOCS

Shape(symmetric, skewed right, skewed left), outliers, center (median vs. mean and what it means) spread (standard deviation (varies ___ away from the mean), IQR(spread of inner 50%), and range (spread of all the data).

stemplot

shows each data value separated into two parts: a stem, which consists of all but the final digit and a leaf, the final digit The stems are ordered from lowest to highest and arraigned in a vertical column.

histogram

shows each interval of values as a bar. The height of the bars show the frequencies or relative frequencies of values in each interval.

statistic

a number that describes some characteristics of a sample

parameter

a number that describes some characteristic of a population

resistant measure

a statistical measure that is not sensitive to extreme values.

standard deviation

measures the typical distance of the values in a distribution from the mean. It is calculated by finding an average of the squared deviations and then taking the square root.

variance

the average squared deviation. To calculate standard deviation

\-find the mean

\-calculate the deviation of each value (value-mean)

\-square each of the deviations then divide by n-1

\-take the square root to return to original units.

box plot

a visual representation of the 5 number summary

marginal relative frequency

when you take one of the totals of a variable, and divide it over the total of subjects

joint relative frequency

the value of a joint variable (so a, one of the singular numbers not a total) and put it over the total of subjects.

conditional relative frequency

putting the a variable over the total of one variable (b).