AP Stats Unit 1

Frequency table

Shows the number of individuals having each value

Relative frequency table

Shows the proportion or percent of individuals having each value

Bar graph

Shows each category as a bar. The heights of the bar show the category(frequency table) frequencies or relative frequencies

Pie chart

shows each category as a slice of pie. The areas of the slices are eproportional to the category(frequency table) frequencies or relative frequencies.

Misleading 

pictographs: have different areas, making some look bigger

vertical scale: may not start at 0 

intervals: all intervals may not be consistently spread out

Two-way table

summarizes data on the relationship between two categorical variables for some group of individuals 

categorical data

data that represents categories, labels or qualities. Doesn’t have mathematical meaning.

ex: eye color, yes/no responses,car brand

quantitative data

Data that represents numbers and quantities. Can be discrete (finite, whole numbers, countable) or continuous(measurable , any value within a range, )

ex:height, weight, hours studying

Marginal relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable.

Joint relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for another.

Conditional relative frequency

gives the percent or the proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable(the condition). 

side by side bar graph

displays the distributions of a categorical variable for each value of another categorical variable. The bars are grouped together based on the values of one of the categorical variables and placed side by side. 

segmented bar graph

displays the distribution of a categorical variable as segments of a rectangle, with the area of each segment proportional to the percent of individuals in the corresponding category. 

mosaic plot

a modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category. 

Association

between two variables if knowing the value of one variable helps us predict the value of the other. If knowing the value of one variable does not help us predict the value of the other, then there is no association between the variables. 

Dotplot

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

symmetric

if the right side of the graph 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

skewed left

if the left side of the graph is much longer than the left side.

How to describe distributions

Shape- Approx symmetrical, skewed right, skewed left 

Outlier: lower fence(Q1 - 1.5x IQR), upper fence(Q3+1.5xIQR). If it is below or above those ranges, it is an outlier. Als,o multiple first. 
Center: median(center value)  or Mean total of all values/ total number of values. Mean for approximately symmetrical and median for skewed data because it is resistant to outliers and gives us a more accurate center. 
Spread: range (max - min) 

Stemplot

shows each 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 arranged in a vertical column. The leaves are arranged in increasing order out from the appropriate stems. (make sure to include a key)

Histogram

shows each interval of values as a bar. The heights of the bars show the frequencies or relative frequencies of values in each interval. (bars are connected)

Mean

the mean of a distribution of quantitative data is the average of all the individual data values. To find the mean you add all the values and dived by the total number of data values. 

Statistic

is a number that describes some characteristic of a sample

parameter

is a number that describes some characteristic of a population

Resistant

A statistical measure is resistant if it isn’t sensitive to extreme values(outliers)

Median

is the midpoint of a distribution, the number such that about half the observations are smaller and about half are larger. 

if the number of values is odd, the median is the middle value in the ordered list

if the number of values is even, the median is the two middle values added and divided by two. 

Range

the distance between the minimum value and the maximum value.

Standard Deviation

measures the typical distance of the values in a distribution from the mean.

Variance

the average squared deviation is called the variance. (standard deviation but without a squared root)

quartiles

divide the ordered data set into four groups having roughly the same number of values, to find the quartiles, arrange the data values from smallest to largest and find the median. 

first quartile

the median of the data values that are to the left of the median in the ordered list

third quartile

the median of the values that are to the right of the median in the ordered list

Interquartile range

the distance between the first and third quartiles of a distribution

Five number summary

a distribution of quantataive data consists of the minimun, the first quartile, the median,the third quartile, and the maximum. 

Boxplot

a visual representation of the five number summary. Calculate the fences and thats were the line ends.The outliers are shown outside of the fences as points on the number line.