# Chapter 2 Descriptive Statistics 2 2 More Graphs

• Slides: 15

Chapter 2 Descriptive Statistics

2. 2 More Graphs and Displays Stem and Leaf Pie Chart Scattered Plot Pareto Time Series graph Dot Plot

A Stem and Leaf plot is a way to display quantitative data. This is a relatively new method way of displaying data. In a stem and leaf plot , each number is separated into a stem (the leftmost digit or digits) and leaf (the rightmost digits) Stem values Leaf values 19 22 25 26 27 28 29 30 34 36 37 42 43 44 46 48 48 49 52 53 55 57 58 62 Benefit: A stem and leaf plot is similar to a histogram except all of the original data is still there (not embedded in classes or buckets)

Example Stem and Leaf plot In 2013 Major league first basemen hit the following number of homeruns: 25, 30, 22, 14, 15, 17, 53, 36, 20, 20, 44, 17, 15, 21, 36, 22, 23, 24, 23 Step 1 : decide on the stems Since the data includes 10 s, 20 s, 30 s, 40 s and 50 s your stems will be 1, 2, 3, 4, and 5 1 2 3 4 5 5 2 0 Data can be ordered or unordered

A dot plot is another way to display quantitative data. Data is displayed above a horizontal axis. Each dot is a single instance of the corresponding number on the x axis Four instances of 25 Horizontal axis should extend to cover all data, even outliers Outliers are unusual data. They don’t seem to fit in the data set An example of an outlier in the data set above would have been a number > 40

Example Dot Plot In 2013 Major league first basemen hit the following number of homeruns: 25, 30, 22, 15, 17, 53, 36, 20, 20, 44, 17, 15, 21, 36, 14, 23, 24, 23 Step 1 : decide on length of horizontal line Since the minimum number of homeruns was 14 and the max was 53 it has to be at least that long . . 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Pie charts provide a convenient way of looking at qualitative data. A Pie Chart divided into sectors that represent the categories. The area of each sector is proportional to the frequency of each category. Motor Vehicle Occupants Killed in 2001 f Relative Frequency Angle Cars 20, 260 0. 56 202 o Trucks 12, 260 0. 34 122 o 0. 08 29 o Cars 0. 02 72 o Trucks Motorcycles Other 3, 067 610 2% 8% 34% 56% Motorcycles Other Benefit: At a quick glance you can see that most fatalities were from cars

Example Pie Chart In 2008 Crisco conducted a national survey as the pie preference of Americans The study revealed that 9% preferred Cherry, 19% Apple, 12% Pecan, 8% Lemon meringue, 13% Pumpkin, 10% Banana cream and 29% preferred some other pie. The first step is to prepare a frequency distribution chart with relative frequencies. Pie preferences of Americans Apple Pumpkin Pecan Banana cream Cherry Lemon meringue Other Relative frequency 0. 19 0. 13 0. 12 0. 1 0. 09 0. 08 0. 29 Other 29% Apple 19% Pumpkin 13% Lemon meringue 8% Pecan 12% Cherry 9% Banana cream 10% The next step is to, starting at 12: 00 (straight up), insert appropriately sized sectors.

Another way to graph qualitative data is to use a Pareto chart A Pareto chart is a vertical bar in which the height of each bar represents the frequency or relative frequency. To construct you will need to construct a frequency table June Car Sales 70 Dollars in thousands Domestic car sales for June 2014 Vehicle Sales in thousands Ford F series 60 Chevrolet Silverado 43 Toyota Camry 40 Ram Pickup 33 Honda Accord 32 Honda Civic 32 Toyota Corolla 31 Ford Fusion 27 Ford Focus 26 Honda CRV 26 60 50 40 30 20 10 0 Ford F series Chevrolet Silverado Toyota Camry Ram Pickup Honda Accord Honda Civic Toyota Corolla Ford Focus Honda Fusion CRV Good form is to have data in descending order Pareto graphs are the most frequently used in the business world

Example Pareto Chart/Graph According to Business Life the 10 richest Hollywood male actor/celebrities are: Arnold Swarzenegger(\$300 M), Tom Hanks(\$350 M), Jack Nicholson(\$385 M), Merv Griffin(\$1000 M), Shakruch Khan(\$600 M), Michael Douglass(\$290 M), Johnnie Depp(\$360 M), Sylvester Stallone(\$430 M), Tom Cruise (\$400 M) and Mel Gibson(\$640 M). To make a Pareto you will need to put them and their respective earnings in a table…in descending order Richest Actors gl as S ld ou D el ha ic an no ks p H m To Ar M Jo hn ni e D lso ho ic N k Ja c ep n se ui ne Cr To m an St al lo Kh Sy lv es to r bs ru k Sh ak Gi el M v Gr iff in on 1200 1000 800 600 400 200 0 er \$\$\$s in Millions Dollars (\$\$\$) in Millions 1000 640 600 430 400 385 360 350 300 290 M Actor Merv Griffin Mel Gibson Shakruk Khan Sylvestor Stallone Tom Cruise Jack Nicholson Johnnie Depp Tom Hanks Arnold S Michael Douglas

When one entry in one data set corresponds to one entry in a second data set, the sets are called Paired sets. One way to graph paired data is to use a scattered plot. A scattered plot shows the relationship between two quantitative variables. The example below is a restaurant owner who recorded the temperature and his ice cream sales for 10 days. Paired sets 58 61 53 59 65 72 67 77 74 69 73 63 Ice Cream Sales in \$\$\$s 215 325 185 332 406 522 412 614 544 421 445 408 700 600 500 \$ in Sales Temp Fo Ice Cream Sales/ Temperature Scatter plot 400 300 200 100 0 77 74 73 72 69 67 65 63 61 Temperatur e in Farenheit 59 58 53

Example Scatter Plot and Paired Data set A teacher asked her students to write the number of hours they had studied at the bottom of a test. After grading she put the scores and hours studied in a paired data matrix Study Hours 1 1 2 2 3 5 6 7 7 7 Study vs Final Score graph 8 7 Hours studied Score 50 40 75 65 80 90 85 100 6 5 4 3 2 1 0 0 20 40 Score 60 80 100 She then graphed the points to look for trends She decided that the hours studied would be the y axis, and the score would be the x axis………but this was just a preference.

A data set that is composed of quantitative entries taken at regular intervals is Time Series. You can use a time series chart to graph a time series. The chart below breaks time down in year and season (x axis) and production in thousands of tons (y axis).

Example Time Series A teacher assigned her students to do a time series graph for the 21 st century Dow Jones highs. The first thing the student does is make a table full of ordered pairs (years and highs) of data from the Dow Jones Industrial site. Dow Jones History 18000 16000 Yearly Index High Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Dow Jones Yearly high 11000 11300 10600 10000 10600 10700 10900 14100 13000 10500 11200 12800 13500 16200 17000 14000 12000 10000 8000 6000 4000 20002001200220032004200520062007200820092010 2011 20122013 2014 Next, plot each ordered pair on a line graph

Graph the following Data. Use the appropriate graphs. Year 2008 2004 2012 1992 2000 1996 1984 1988 1980 1976 Voters in million voters 131 122 121 106 105 96 93 92 86 81 New Mexico Nevada Texas Oregon Wyoming Alaska Colorado Arizona Montana California 121, 589 sq mi 110, 560 sq mi 268, 580 sq mi 98, 380 sq mi 97, 813 sq mi 663, 267 sq mi 104, 093 sq mi 113, 998 sq mi 147, 042 sq mi 163, 695 sq mi