Stats Chapter 2

Cumulative Frequency Polygon

X axis = Cumulative Frequency (# of vehicles sold) y axis = profit Vertical axis on right = Cumulative relative frequency (% of vehicles sold) *look at image on slide

Pie Charts and Bar Charts..

both serve to illustrate frequency and relative frequency tables

Step 2 Determine the class intervals Example: Applewood Auto

i > and/or = (highest value- lowest value)/8 (3,292-294)/8= $374.75 *round up to some convenient 8 is from (Recommended Classes from Step 1)

Pie Chart

*Use a pie chart to compare relative differences in the percentage of observations for each class of a qualitative variable. -shows the proportion or percentage that each class represents of the total number of frequencies

Bar Chart

*Use when you wish to compare the number of observations for each class of a qualitative variable - shows the qualitative classes on the horizontal axis and class frequencies on the vertical axis -The class frequencies are proportional to the height of the bars -most common

Step 3: Set the individual class limits Example: Applewood Auto

*lower limits should be rounded to an easy to read number when possible Classes 200 up to 600 600 up to 1,000 1,000 up to 1,400 etc until 8 classes (Step 1) added about 400 (Step 2)

Histogram

-A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. -The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other *shows the shape of a distribution

Step 4: Tally the data into classes and determine the Number of observations in each class Example: Applewood Auto

-The number of the observations is the class frequency 200 up to 600= 8 600 up to 1000 =11 1000 up to 1400= 23 etc Total 180

How to find Relative Frequency

-To find the relative frequencies simply take the class frequency and divide by the total number of observations 200 to up 600___= 8 /180= .004 600 up to 1000__ = 11 /180= .061 1000 up to 1400 ___= 23 /180= .128 1400 up to 1800_____= 38 /180= .211 Etc Total 180 ------------------1.000

Relative Class Frequencies

-can convert class frequencies to relative frequencies to show a fraction of the total number of observations in each class -captures the relationship between class frequency and total Number of observations

Frequency Polygon

-shows the shape of the distribution, similar to a histogram -consist of line segments connecting the points formed by the intersections of the class midpoints and class frequencies -Vertical axis: Frequency -Horizontal Axis Profit (Midpoints) *good to use when comparing 2 or more distributions

4 Steps

1) Decide on the number of classes 2) Determine the class intervals 3) Set the individual class limits 4) Tally the data into classes and determine the Number of the observations in each class

Midpoint

200 up to 600 (PROFIT) 200+600/2 = 400 (MIDPOINT) 8 (FREQUENCY)

Step 1: Decide on the number of classes

2^k > n K is the number of classes n is the number of values in the data set Example: Applewood Auto sold 180 cars n=180 2^8=256 > 180 Recommended Classes is 8

Frequency Distribution

A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

Frequency Table

A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

How to find Cumulative Relative Frequency

Cumulative Frequency Founded by 8_____ 8 19______8+11 42______ 8+11+23 80______ 8+11+23+38 Cumulative Relative Frequency 8/180 =0.044= 4.4% 19/180= 0.106= 10.6% *divide cumulative frequency by the total number of observations

Difference between Bar Graph and Histogram

Histogram presents numerical data whereas Bar graph shows categorical data

Relative Frequency Example:

Kane 52 /180= .289 Olean 40 /180= .222 Sheffield 45 /180= .250 Tionesta 43 /180=.239 Total: 180 1.000 *each of the class frequencies is divided by the total number of observations

Frequency Table: for Number of Vehicles sold last month at Apple wood Auto group by location

Location Number of Cars Kane 52 Olean 40 Sheffield 45 Tionesta 43 TOTAL: 180

How to find Cumulative Frequency Distributions

Q Sixty of the vehicles earned a profit of less than what amount? Profit_____________Frequency 200 up to 600 ____8 600 up to 1000_____ 11 1,000 up to 1400____ 23 etc Total 180 Cumulative Frequency Founded by 8______ 8 19_______ 8+11 42_____ 8+11+23 80 ________8+11+23+38

How to find percentages for Pie Chart? Example Vehicle sales by type at Applewood auto group

Type Sold % Sedan 72/180 x 100 = 40% SUV 54/180 x 100 = 30% Compact 27/180 x 100 = 15% Truck 18/180 x 100 = 10% Hybrid 9/180 x 100 = 5%