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AP Statistics Chapter 1
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Exploring Data
Terms in this set (45)
The 1.5 x IQR Rule for Outliers
Call an observation an outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile
Association
Occurs between two variables if specific values of one variable tend to occur in common with specific values of the other
Back-to-back stemplot
Used to compare the distribution of a quantitative variable for to groups. Each observation in both groups is separated into a stem, consisting of all but the final digit, and a leaf, the final digit. The stems are arranged in a vertical column with the smallest on the top. The values from one group are plotted on the left side of the stem and the values from the other group are plotted on the right side of the stem. Each leaf is written in the row next its stem, with the leaves arranged in increasing order out from the stem.
Bar graph
Used to display the distribution of a categorical variable or to compare the sizes of different quantities. The horizontal axis of a bar graph identifies the categories or quantities being compared. Drawn with blank spaces between the bars to separate the items being compared.
Bimodal
Describes a graph of quantitative data with two clear peaks
Boxplot
A graph of the five-number summary. The box spans the quartiles and shows the spread of the central half of the distribution. The median is marked withing the box. Lines extend from the box to the extreme and show the full spread of the data.
Categorical Variable
Places an individual into one of several groups or categories
Conditional distribution
Describes the values of one variable among individuals who have a specific value of another variable. There is a separate conditional distribution for each value of the other variable.
Data analysis
A process of describing data using graphs and numerical summaries
Dotplot
A simple graph that shows each data value as a dot above its location on a number line
Distribution
Tells what values a variable takes and how often it takes these values
Distribution
Tells what values a variable takes and how often it takes these values
First quartile Q1
If the observations in a data set are ordered from lowest to highest, the first quartile Q1 is the median of the observations whose position is to the left of the median
The Five-Number Summary
Consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest. In symbols, the five-number summary is Minimum Q1 M Q3 Maximum
Frequency table
Displays the count (frequency) of observations in each category or class
Histogram
Displays the distribution of a quantitative variable. The horizontal axis is marked in the units of measurement for the variable. The vertical axis contains the scale of counts or percents. Each bar in the graph represents an equal-width class. The base of the bar covers the class, and the bar height is the class frequency or relative frequency.
Individuals
Objects described by a set of date. Individuals may be people, animals, or things.
Inference
Drawing conclusions that go beyond the data at hand
Interquartile range
IQR=Q3-Q1
Marginal distribution
The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table.
Mean
The arithmetic average. To find the mean of a set of observations, add their values and divide by the number of observations.
Median M
The midpoint of a distribution, the number such that half the observations are smaller and the other half are larger. To find the median of a distribution: 1. Arrange all observation in order of size, from smallest to largest. 2. If the number of observations n is odd, the median M is the center observation in the ordered list. 3. If the number observations n is even, the median M is the average of the two center observations in the ordered list.
Mode
The value or class in a statistical situation distribution having the greatest frequency
Multimodal
Describes a graph of quantitative date with more than two clear peaks
Outlier
An individual value that falls outside the overall pattern of a distribution
Overall pattern
In any graph of data, look for the overall pattern and for striking departures from that pattern. Shape, center, and spread describe the overall pattern of the distribution of a quantitative variable.
Pie chart
Shows the distribution of a categorical variable as a "pie" whose slices are sized by the counts or percents for the categories. A pie chart must include the categories that make up a whole.
Quantitative Variable
Takes numerical values for which it makes sense to find an average
Range
The range of a set of quantitative data is the maximum value minus the minimum value
Relative frequency table
Shows the percents (relative frequencies) of observations in each category or class
Resistant measure
A statistic that is not affected very much by extreme observations
Roundoff error
The difference between the calculated approximation of a number and its exact mathematical value
Segmented bar graph
Used to compare the distribution of a categorical variable in each of several groups. For each group, there is a single bar with "segments" that correspond to the different values of the categorical variable. The height of each segment is determined by the percent of individuals in the group with that value. Each bar has a total height of 100%.
Side by side bar graph
Used to compare the distribution of a categorical variable in each of several groups. For each value of the categorical variable, there is a bar corresponding to each group. The height of each bar is determined by the count or percent of individuals in the group with that value.
Simpson's paradox
An association between two variables that holds for each individual value of a third variable can be changed or even reversed when the data for all values of the third variable are combined
Skewness
A distribution is skewed to the right if the right side of the graph (containing half of the observations with larger values) is much longer than the left side. It is skewed to the left if the left side of the graph is much longer than the right side.
Splitting stems
A method for spreading out a stemplot that has two few stems
Standard deviations sx
Measures the average distance of the observations from their mean. It is calculated by finding an average of the squared distances and then taking the square root. (Insert super long complicated equation)
Stemplot
A simple graphical display for fairly small data sets that gives a quick picture of the shape of a distribution while including the actual numerical values in the graph. Each observation is separated into a stem, consisting of all but the final digit, and a leaf, the final digit. The stems are arranged in a vertical column with the smallest at the top. Each leaf is written in the row to the right of its stem, with the leaves arranged in increasing order out from the stem
Symmetry
If the right and left sides of a graph are approximately mirror images of each other.
Third quartile Q3
If the observations in a data set are ordered from lowest to highest, the third quartile Q3, is the median of the observations whose position is to the right of the median.
Two-way table
A two-way table of counts organizes data about two categorical variables
Unimodal
Describe a graph of quantitative data with a single peak
Variables
Any characteristic of an individual. A variable can take different values for different individuals.
Variance s^2x
The average squared distance of the observations in a data set from their mean. (Insert super long and complicated equation)
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