stats 227 exam 1 chapt 1-2

Features of a stem plot

shows the shape of the distribution of data, retains the original data values, the sample data are sorted (arranged in order)

Cencus

the collection of data of everymember of the population

population

the complete collection of all mesurments or data that are being considered.

skewed right (positively skewed)

the graph has a tail that elongates to the right. *the mode is less than the median which is less than the mean

Class boundaries

the numbers used to separate the classes, but without the gaps created by class limits 124.5 174.5 to24.5 and 274.5 are in the center of these gaps the lowest class boundary is 74.5 and the highest class boundary is 324.5. The complete list of class boundaries is 74.5 124.5 174.5 224.5 274.5 and 324.5

Statistics

the science of planning studies and experiments, obtaining data and the organizing summarizing presenting analayzing and then interpreting those data and then drawing conclusion based on it.

Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?

yes

linear correlation

exists between two variables when there is a correlation and the plotted points of paired data result in a pattern that can be approximated by a straight line

Correlation

exists when The values of one variable or somehow associated with the values of the other variable

Presented for a class

frequency for a class/ some of all frequencies*100

Class width equation

max data value -min data value/ number of classes

Quantitative data

numbers representing counts or measurements

discrete data

data values are quantitative and finite or concrete

stem and leaf plot

Represents quantitative data by separating each value into two parts (the stem the left most digit) and the leaf the (right most digit)

Skewed Left Distribution

(negatively skewed) The "tail" of the graph elongates more to the left. The mean is to the left of the median.

data

collection of obsrvations aka datum

Pareteo charts

A bar graph used to draw attention to the more important categories, bars are arranged in descending order according to frequencies vertical scale represents frequencies and horizontal scale identifies the different categories

histogram

A graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in data.) The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. the heights of the bars correspond to frequency values

Time series graph

A graph of Time series data, which are quantitative data that have been collected at different points in time such as monthly or yearly features, reveals information about trends over time

We construct frequency distributions to

One summarize large data sets, to see the distribution and identify outliers, and three have a basis for constructing graphs such as histograms

Upper class limits

Are the largest numbers that can belong to each of the different classes

Lower class limits

Are the smallest number that can belong to each of the different classes

Class midpoints

Are the values in the middle of the classes table 2 - 2 Has midpoints of 95.5, 149.5, 199.5, 249.5 and 299.5 each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2

Bar graph versus histogram

Bar charts each column represents a group defined by categorical variables, histograms each column represents a group defined by quantitative variables

Dot plot

Consists of a graph in which each data value is plotted as a point (or dot) along a scale of values. Dots representing equal values are stacked.

continuous data

Data that can take on any value. There is no space between data values for a given domain. Graphs are represented by solid lines.

categorical data

Data that consists of names, labels, or other nonnumerical values

Features of Dot plots

Displays the shape of the distribution of data, does usually possible to re-create the original list of data values,

frequency

For a particular class is the number of original value that fall into that class

relative frequency for a class

Frequency for a class/some of all frequencies

Relative frequency histogram

Has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies (as percentages or proportions instead of actual frequencies)

Scatterplot

Is a plot of paired X, Y quantitative data with a horizontal X axis and a vertical Y axis the horizontal axis is used for the first variable X), and the vertical axis is used for the second variable Y

Class with

Is the difference between two consecutive lower class limits (or two consecutive lower class boundaries) in the frequency distribution table 2-2 uses a class width of 50 ( the first to lower class boundaries are 75 and 125 and there difference is 50)

The sum of percentages in a relative frequency distribution

Must be close to 100 with a little wiggle room for rounding error's

Graphs that deceive

Nonzero Axis: Graphs can be misleading because one or both of the axes begin at some value other than zero, so that differences are exaggerated. slso pictogrpahs b/c Artist can create false impressions that grossly distort differences by using simple principles of basic geometry

frequency distribution (or frequency table

Shows how data or partitioned among several categories by listing the categories along with the number (frequency) or data values in each of them

Cumulative frequency distribution

The frequency for each class is the sum of the frequencies for that class and all previous classes

ratio

data can be arranged in some order, diff.s ( via subtraction0 b/t data values can be measured and are meaningful natural zero starting pt exists, representing that none of the qty is present

nominal

data consistent of names labels or catagories only

interval scale

data is categorized by rank but also the distance between categories can be measured (via subtraction) and there is no absolute zero

Bar graphs

Uses bars of equal width to measure categorical data. vertical scales represent frequencies or relative frequencies, horizontal skills represent different categories bars may or may not be separated by small gaps could contain multiple bars

frequency polygon

Uses line segments connected to points directly above class midpoint values Very similar to a histogram but a frequency polygon uses line segments instead of bars

Important uses of histograms

Visually displays the shape of the distribution of the data, shows the location of the center of the data, shows the spread of the data, and identifies outliers.

skewed data

When a set of data is not symmetrical it can skewed, meaning it tends to have a long tail on the left or right side.

Does the frequency distribution appear to have a normal distribution? Explain

Yes because the frequency start low proceed to one or two high frequencies then decreased to a low frequency and the distribution is approximately symmetric

Pareto Chart

a bar graph whose bars are drawn in decreasing order of frequency or relative frequency feats: Shows the relative distribution of categorical data so that it's easier to compare the different categories, draws attention to more important categories

Parameter

a numerical measurement describing some characteristic of a population

Statistics

a numericalmeasurement describing some characteristic of a sample

ordinal scale

a scale of measurement in which the measurement categories form a rank order along a continuum. subtraction-cannot be measured in this method

sample

a sub collection of every of members selected from the pop.

pie chart

a type of graph in which a circle is divided into sectors that each represent a proportion of the whole. In which the size of each slice is proportional to the frequency count for the category

bell-shaped distribution

bell shaped means normal distribution