Chpt 2 Frequency Distributions and Graphs 2-4 Pareto chart, time series graph, Pie chart 1
Chpt 2 2-4 Read pages 63-77 p76 Applying the Concepts p77 1, 7, 9, 11, 13, 14, 15 Homework 2
Chpt 2 Objectives Represent data using Bar Graphs, Pareto Charts, Time Series Graphs, and Pie Graphs. 3
More Graphical Objective: Represent data using Pareto Representations Pareto Chart Time Series Graph Pie Chart (Pie Graph) Stem and Leaf Plot 4
Bar Graph A bar chart is very much like a histogram. A bar chart is strictly used with categorical data. With no continuity, there are gaps between the bars. The height of the bar represents the frequency of the class. 5
Pareto Chart Pareto charts - a Pareto chart is used to represent a frequency distribution for a categorical variable. Used with Categorical (Nominal) Data Bar chart with classes arranged in descending order of frequency (highest to lowest) Make the bars the same width. Make the units that are used for the frequency equal in size. 6
Pareto Chart 7
Time Series Graph A time series graph represents data that occur over a specific period of time. Frequency Polygon Horizontal axis = time (year, month, day, hour, etc.) Designed to show trends of data over time 8
Time Series Graph 9
Time Series Graph 10
Pie Graph (Pie Chart) A pie graph (pie chart) is a circle that is divided into sections or wedges representing the relative frequencies in each category of the distribution. Circle with wedges (slices) indicating portion representing class relative frequency. Shows proportions, highlights portion of whole population First appeared with line graph and bar chart in late 18 th century from William Playfair (Scotland) Made famous by Florence Nightingale during Crimean War. 11
Pie Graph (Pie Chart) To determine size of slice f = m α total 360 Relative frequency 360 = α (central angle of slice) Determine the appropriate central angle for each of the categories in the table. Yellow 2/23 32 Black 1/23 15 Color f Rel f Blue 9 9/23 Red 6 6/23 Green 5 5/23 Yellow 2 2/23 Black 1 1/23 9 = m α 23 360 α 141 94 78 32 15 Green 5/23 78 Red 6/23 94 Blue 9/23 141 12
Stem and Leaf Plot A stem and leaf plot (stemplot) is a data plot that uses part of a data value as the stem and part of the data value as the leaf to form groups or classes. A stemplot has the advantage over grouped frequency distribution of retaining the actual data while also showing them in graphic form. Keeps the data List the data using part of the data (stem) as a class and the last single digit of the data value (leaf). To read the data value attach the leaf to the stem. 13
Stem and Leaf Plot 32, 18, 47, 65, 22, 33, 64, 44, 32, 15, 9, 16, 48, 77, 31, 25, 28, 55, 56, 12, 7, 10, 28, 22, 65, 47, 18, 32, 55, 15, 44 0 9 7 0 7 9 1 8 5 6 2 0 8 5 1 0 2 5 5 6 8 8 2 2 5 8 8 2 2 2 2 5 8 8 3 2 3 2 1 2 è 3 1 2 2 2 3 4 7 4 8 7 4 4 4 4 7 7 8 1 2 = 12 5 5 6 5 5 5 5 6 6 5 4 5 6 4 5 5 Be sure to include a 7 7 7 7 key for the stemplot 14
Stem and Leaf Plot 12.3, 6.2, 12.4, 9.8, 15.7, 7.4, 6.4, 7.7, 8.5, 10.5, 9.1, 11.0 6 2 4 DO NOT FORGET to include 7 4 7 6 2 = 6.2 8 5 a key for the stemplot 9 1 8 10 5 11 0 12 3 4 5 15
Words of Caution Graphs represent data using pictures (worth a thousand words) but sometimes the words perceived by the reader may not be accurate. 16
Words of Caution Clever may lead to different perception Who eats more cantaloupe, men or women? Servings per Month 3 2 1 0 The observer sees this in two dimensions, but only one dimension has relevance. Male Female Ensure the area of the display has the appropriate proportion. 17
Words of Caution Make certain the display is complete The graph should have a title explaining the subject. Horizontal & Vertical axes should be clearly labeled Missing labels show no information. Graphs should also include source reference 18
Huh? 19
Forest - Trees Who can make sense of this? 20
Maybe 21
37 > 37 49 > 50 22
26 26 23
Soared? 24
Magic Objective: Represent data using Pareto 25
This Just In hlp://www.ed-data.org/state/ca/ps_nzg2oq%5e%5e 26
TI-84 Objective: Represent data using Pareto Window Key 2 nd TBLSET Y = Key 2 nd STAT PLOT 2nd Key MATH Key x 2 Key 2 nd On Key 2 nd OFF Trace Key 2 nd CALC Scrolling arrows 2 nd Screen contrast Stat Key 2 nd LIST VARS Key 2 nd DISTR ^ (Carat) Key +,,, Keys Enter Key 27
TI-84 BASIC INSTRUCTIONS First turn it on 2 nd ON will turn it off Let us put in your name PRGM NEW ENTER ALPHA YOURNAME ENTER 2 ND QUIT 28
TI-84 Return to home screen 2 ND QUIT Basic arithmetic operations (4+5) (4 5) 4 + 5 ENTER 4 x 5 ENTER (4 5) 4 5 ENTER 4 2 OR 4 x 2 ENTER 4 ^ 2 ENTER 29
TI-84 More basic arithmetic operations (4 5 ) 4 ^ 5 ENTER 4 2 ND 4 ENTER 4 + 3 2 ND 4 + 3 ENTER 4 + 3 2 ND 4 + 3 ENTER If you prefer your answer in fraction form MATH 1:>Frac ENTER 30
TI-84 To create a list (6 preinstalled lists) STAT 1:EDIT Select List Enter first datum ENTER Repeat to end of list 2 ND QUIT To clear a list STAT 1:EDIT Select List To Heading CLEAR ENTER Or NOT DELETE STAT 4:ClrList 2 ND List Number ENTER 31
TI-84 Enter the data from your wingspans Stat 1:Edit Select List L1 Enter first value 20 Enter Enter 2nd value 30 Enter Repeat to end of list To draw a histogram of your data values (STAT PLOT) L1 2nd y= Enter ON TYPE: XList 2nd 1 Freq: 1 Zoom 9 32
Using the data from your m&m frequency distribution of the colors of the candies create a bar chart, and pie chart of the colors. Blue Brown Green Orange Red Yellow Repeat for Skittles. 33