Chapter 1 Vocab AP Statistics

Segmented bar graph

A 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

Resistant

A statistical measure is resistant if it isn't sensitive to extreme values.

Boxplot

A Boxplot is a visual representation of the five-number summary.

Five-number summary

A Five-number summary of a distribution of quantitative data consists of the minimum, the first quartile Q1, the median, the third quartile Q3, and the maximum.

Histogram

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

Stemplot

A 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 arranged in a vertical column. The leaves are arranged in increasing order out from the appropriate stems.

Range

The range of a distribution is the distance between the minimum value and the maximum value. That is, Range = Maximum - Minimum

bar graph

shows each category as a bar. The heights of the bar show the category frequencies or relative frequencies

pie chart

shows each category as a slice of pie

Frequency table

shows number of individuals having each value

relative frequency table

shows proportion or percent of individuals having each value

two way table

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

Skewed Distribution - Left

A distribution is skewed to the left if the left of the graph is much longer then the right side

Skewed Distribution - Right

A distribution is skewed to the right if the right side of the graph is much longer than the left side

Dotplots

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

Symmetric Distribution

Any distribution is roughly symmetric if the right side of the graph (containing the half of observations with The largest values) is approximately a mirror image of the left side

Side-By-Side bar graph

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

Distribution

Tells us what values the variable takes and how often it takes those values

Median

The Median is the midpoint of a distribution, the number such that about half of the observations are smaller and about half are larger. To find the median, arrange the data values from smallest to largest. - if the number n of data values is odd, the median is the middle value in the ordered list. - if the number n of data values is even, the median is the average of the two middle values in the ordered list.

Quartiles

The Quartiles of a distribution 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. The first quartile Q1 is the median of the data values that are to the left of the median in the ordered list. The third quartile Q3 is the median of the data values that are to the right of the median in the ordered list.

Standard Deviation

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

Interquartile range (IQR)

The interquartile range (IQR) is the distance between the first and the third quartiles of a distribution. In symbols: IQR = Q3 - Q1

The mean x̅

The mean x̅ (pronounced "x-bar") of a distribution of quantitative data is the average of all the individual data values. To find the mean, add all the values and divide by the total number of observations. if the n observations are X1, X2, ......, Xn, the mean is given by the formula x̅ = sum of data values / number of data values = (X1 + X2 + ..... + Xn) / n = ΣXi / n

Association

There is an association between two variables if knowing the value of one variable helps us predict the value 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.

marginal relative frequency

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

conditional relative frequency

gives the percent or 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)

joint relative frequency

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