Math 146 Intro to Statistics questions and answers

explanitory variable

(x)

response variable

(y) a variable that measures an outcome or result of a study

Data

any collection of numbers, characters, images or other items that provide information about something.

respondents

individuals who answer a survey

subjects

the people or animals participating in a research project

experimental units

animals, plants, websites, or other inanimate objects

records

Rows in the table

Example purchase records

who

people on whom we experiment or (subjects) / cases

how

How data was collected

Variable

a characteristic or attribute that can assume different values

categorical variable

a variable that names categories (whether with words or numerals)

Example : numeral categorical variable : Area Code

nominal variables

A variable whose values are used only to name categories.

categorical variables because they name categories

quantitative variable

a characteristic that can be measured numerically

identifier

an attribute whose value is associated with one and only one entity instance

Example: Alive or Dead

Student ID Number

ordinal variable

Variables that report order without natural units

model for data

Models are summaries and simplifications of data that help us understand.

what

"what" are the variables

why

helps you decide which way to treat the variables

area principle

the area occupied by a part of the graph should correspond to the magnitude of the value it represents

frequency table

A table that uses numbers to record data.

relative frequency table

Shows the percents or proportions (relative frequencies) of observations in each category or class.

The sum of the percentages need to add up to 100%

bar chart

gives an accurate visual impression of the distribution because it obeys the area principle.

pie chart

Displays a circle is divided into sectors which shows a percentage of a whole.

ring chart

or donut chart that is a modified form of pie chart that displays the "crust" of the pie.

Histogram

A graph of vertical bars representing the frequency distribution of a set of data.

stem and leaf display

is like a histogram, that shows the distribution of quantitative variables, but shows the distribution with individual values.

Dotplot

A simple graph that shows each data value as a dot above its location on a number line.

Density Plots

are like histograms with smooth bins that reduce the effect of bins in the distribution.

Shape

summarization of the distribution in three attributes.

1. How many modes it has.

2. whether its symmetric or skewed

3. whether it has any extraordinary cases or outliers.

modes

scale pattern. the pattern of hump or humps in a histogram.

the mode is sometimes defined as a single value that appears most often.

unimodal

a histogram with one peak

bimodal

a histogram with two peaks

multimodal

a distribution with three or more peaks in the histogram

uniform

The same all the way through; consistent

a histogram that doesnt appear to have any mode and in which all the bars are approximately the same height.

symmetric

Being equal or the same in size, shape, and relative position

tails

thinner ends of a distribution

skewed distribution

When the results are not symmetrical (appears to favor one side over the other)

if one tail stretches out farther than the other.

skewed right distribution

The peak of the data is to the left side of the graph. There are only a few data points to the right side of the graph.

the distribution tail is stretched out to the right

Skewed Left Distribution

The peak of the data is to the right side of the graph. There are only a few data points to the left side of the graph.

the distribution tail is stretched out to the left.

Outliers

extreme values that don't appear to belong with the rest of the data

Median

the middle score in a distribution; half the scores are above it and half are below it

the value of the distribution in the middle.

if (n) is odd the median is the middle value.

If (n) is even the median is the average of the two values in the middle.

mean

the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores

the point where the histogram is balanced.

range

the difference between the highest and lowest scores in a distribution

how you measure the spread.

Range = max - min

IQR (interquartile range)

measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, IQR = Q3 − Q1.

ALMOST ALWAYS A REASONABLE SUMMARY OF SPREAD

Lower Quartile (Q1)

First Quartile

25th percentile

the median of the lower half of the data set

the value that is just above the lower 25% of the data values.

Upper Quartile (Q3)

3rd quartile

75th percentile

the value that is 75% or 75th percentile.

Median (50th percentile)

is the 50th percentile or second quartile.

standard deviation

takes into account how far each value is from the mean.

take the results of variance and square root it to get the standard deviation

least-squares property

sum of the squares of the residuals is the smallest sum possible

Residuals

the differences of the values from the mean.

variance

standard deviation squared

when you add up the squared residuals and divide by n-1, the result is the variance, denoted s^2 (s squared)

Conditional distribution

questions that restrict our attention to just one condition of a variable and ask about the distribution of another variable are asking about the conditional distribution.

conditional distribution show the distribution of one variable for only the cases that satisfy a condition on another variable.

Indipendent variable

in a contingency table, when the distribution of one variable is the same for all categories of another, the variables are independent. (there's no association between these variables.)