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