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Algebra 2 Statistics Unit

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Normal Distribution

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Mar 1, 2020

Cards (98)

Section 1

(50 cards)

Normal Distribution

Front

Is completely specified by two numbers, mean μ and standard deviation σ.

Back

median (M)

Front

midpoint of a distribution, typical value; in a skewed distribution, the mean is usually farther out

Back

distribution

Front

describes what values the variable takes and how often it takes them

Back

Correlation

Front

Measures the direction and strength of the linear relationship between two quantitative variables.

Back

IQR

Front

measures the range of the middle 50% of the data; IQR=Q3-Q1; resistant

Back

Negative association

Front

Above-average values of one variable tend to accompany below-average values of the other, and vice versa.

Back

describing a distribution of quantitative data

Front

SOCS (Shape-Outlier-Center-Spread)

Back

Density curve

Front

A curve that (a) is always on or above the horizontal axis, and (b) has exactly 1 area underneath it.

Back

outlier

Front

individual value that falls outside the overall pattern; it is an outlier if it is more than 1.5 x IQR above the third quarter or below the first quartile

Back

five-number summary; summary of spread and center

Front

Minimum, Q1, M, Q3, Maximum

Back

Explanatory variable

Front

A variable that may help explain or influences changes in a response variable.

Back

bimodal

Front

two clear peaks

Back

First Quartile (Q1)

Front

one quarter up the list; resistant

Back

skewed to the right

Front

if the right side of the graph with larger values is longer than the left

Back

histogram

Front

plot the counts (frequencies) or percents (relative frequencies) of values in a equal-width classes; show distribution of a quantitative variable

Back

dotplot

Front

individual values on a number line; show distribution of a quantitative variable

Back

relative frequency table

Front

the distribution of a categorical variable lists the categories and gives the percent of individuals that fall in each category

Back

Describing a scatterplot

Front

Can be described by the direction, form, and strength of the relationship.

Back

Pth percentile

Front

The value with P percent of the observations less than it.

Back

Third Quartile (Q3)

Front

three-quarters up the list; resistant

Back

pie charts, bar graphs

Front

display the distribution of a categorical variable

Back

Least-squares regression line

Front

Line that makes the sum of the squared vertical distances of the data points from the line as small as possible.

Back

frequency table

Front

distribution of a categorical variable lists the categories and gives the count of individuals that fall in each category

Back

stemplot

Front

separate each observation into a stem and a one-digit leaf; show distribution of a quantitative variable

Back

two-way table

Front

organizes data about two categorical variables; often used to summarize the large amounts of information by grouping outcomes into categories

Back

statistical question

Front

a question that can be answered by collecting data and where there will be variability in that data

Back

x-bar

Front

the mean of a set of observations/sample (add their values and divide by the number of observations), use for reasonably symmetric distributions

Back

Influential Point

Front

An observation that if removed it would markedly change the result of the calculation.

Back

range

Front

subtract the smallest value from largest value

Back

Standardized values (z-scores)

Front

Tells how many standard deviations a data point is from mean

Back

multimodal

Front

multiple peaks

Back

Standard Normal distribution

Front

Has mean 0 and standard deviation 1

Back

mean

Front

arithmetic average, measure of center, NOT RESISTANT MEASURE OF CENTER, average value

Back

standard deviation (s sub-x)

Front

measures the average distance of the observations from their mean; measures spread about the mean, always greater or equal to 0, not resistant, use for reasonably symmetric distributions

Back

Cumulative relative frequency graph

Front

Used to examine location within a distribution. Completed graph shows the accumulating percent of observations

Back

Median of a density curve

Front

Equal areas point

Back

unimodal

Front

single peak

Back

Mean of a density curve

Front

Balance point

Back

boxplot

Front

based on 5 number summary, useful for comparing distributions, shows spread of central half of distribution

Back

marginal distributions

Front

the row totals and column totals

Back

symmetric

Front

the right and left sides of the graph are symmetric

Back

conditional distributions

Front

describes the values of that variable among individuals who have a specific value of another variable. Can be displayed with a SIDE-BY-SIDE BAR GRAPH or a SEGMENTED BAR GRAPH

Back

mean

Front

the average

Back

association

Front

one of the variables tends to occur in common with specific values of the other

Back

mode; modes

Front

most frequent; major peaks

Back

Outlier

Front

An observation that lies outside the overall pattern of the other observations.

Back

numerical summary

Front

should report at least its center and spread, or variability

Back

μ (mu)

Front

a population mean

Back

The 68-95-99.7 Rule

Front

Also known as the "Empirical Rule."

Back

Extrapolation

Front

The use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line.

Back

Section 2

(48 cards)

Lurking variable

Front

A variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied.

Back

Inference about cause and effect

Front

Using experimental results to draw conclusions about causality

Back

Control group

Front

In an experiment, the group that is administered a placebo treatment (an active treatment) or no treatment; results are compared to the treatment group

Back

Slope

Front

The amount by which y is predicted to change when x increases by one unit.

Back

Factor

Front

An explanatory variable in an experiment

Back

Population

Front

The entire aggregation of individuals from which samples can be drawn

Back

Experimental units

Front

the smallest collection of individuals to which treatments are applied

Back

Bias

Front

Occurs when a study design favors some outcomes over others

Back

Regression line

Front

A line that describes how a response variable y changes as an explanatory variable x changes; also known as "line of best fit"

Back

Confidentiality

Front

Any information gathered about a participant must not be revealed without the participants consent.

Back

Experiment

Front

Deliberately imposes some treatment on individuals to measure their responses. Causality can be inferred if carried out well.

Back

y intercept

Front

The predicted value of y when x = 0.

Back

Voluntary Response Samples

Front

A sample that consists of people who choose themselves by responding. They often over represent people with strong opinions. BIAS

Back

Replication

Front

Enough units in each group so that any difference in the effects of the treatments can be distinguished from chance differences between the groups. Reduces sample variability

Back

Convenience Sample

Front

A sample which consists of members of a population that are easily accessed. Generally leads to bias.

Back

Sample

Front

A relatively small proportion of people who are chosen in a survey so as to be representative of the whole.

Back

Single Blind

Front

a study in which the participants are unaware of whether they are in the control group or the experimental group

Back

Residual plot

Front

The distribution of residuals; helps us assess how well a regression line fits the data.

Back

Response variable

Front

A variable that measures an outcome of a study.

Back

Placebo effect

Front

Experimental results are caused by expectations alone; double blindness is intended to mitigate this effect.

Back

Response Bias

Front

Bias that occurs when the behavior of the respondent or of the interviewer causes inaccurate results

Back

Explanatory Variable

Front

a variable that we think explains or causes changes in the response variable

Back

Positive association

Front

Above-average values of one variable tend to accompany above-average values of the other, and below-average values also tend to occur together.

Back

Undercoverage

Front

Occurs when some groups in the population are left out of the process of choosing the sample

Back

Completely Randomized Design

Front

All experimental units have an equal chance of receiving each of the treatments

Back

Sampling Frame

Front

A list of individuals from whom the sample is drawn

Back

Stratified random sample

Front

A method of sampling that involves dividing your population into homogeneous subgroups and taking a simple random sample in each subgroup. Internally homogeneous and externally heterogeneous.

Back

Random sampling

Front

A sample that fairly represents a population because each member has an equal chance of inclusion

Back

Sampling error

Front

An error that occurs when a sample somehow does not represent the target population due to bad sampling methods and/or undercoverage

Back

Anonymity

Front

Even the researcher cannot link participants to their data

Back

Control

Front

In an experiment, the standard that is used for comparison. Reduces lurking variables!

Back

Randomized block design

Front

Form blocks consisting of individuals that are similar in some way that is important to the response. Random assignment of treatments is then carried out separately within each block.

Back

Census

Front

A study that attempts to collect data from every individual in the population.

Back

Double Blind

Front

This term describes an experiment in which neither the subjects nor the experimenter knows whether a subject is a member of the experimental group or the control group.

Back

Elements of Experimental Design

Front

CONTROL, RANDOM ASSIGNMENT, AND REPLICATION

Back

Nonresponse

Front

When the subjects refuse to cooperate or cannot be reached. This leads to non sampling bias.

Back

Cluster Sample

Front

A sample in which a simple random sample of heterogeneous subgroups of a population is selected. Internally heterogeneous and externally homogeneous.

Back

Predicted value

Front

The value predicted by the regression model; read as "y hat"

Back

Statistically significant

Front

Referring to a correlation, or a difference between two groups, that is larger than would be expected by chance alone.

Back

Scatterplot

Front

Plot that shows the relationship between two quantitative variables measured on the same individuals.

Back

Inference about the population

Front

Using sample data to draw conclusions about the population

Back

Block

Front

A group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

Back

Observational study

Front

A study that merely observes conditions of individuals in a population and records information; the population is disturbed as little as possible.

Back

Matched Pair

Front

The most extreme form of blocking. Subjects are matched in pairs as closely as possible and each subject in a pair is randomly assigned to receive one of the treatments.

Back

Residual

Front

The difference between an observed value of the response variable and the value predicted by the regression line.

Back

Confounding

Front

The effect of some variable on the response variable cannot be separated from the effect of the explanatory variable.

Back

Simple Random Sample (SRS)

Front

A sample of size n selected from the population in such a way that each possible sample of size n has an equal chance of being selected.

Back

Random Assignment

Front

Assigning participants to experimental and control conditions by chance, thus minimizing the effects of preexisting differences among those assigned to the different groups.

Back