TN 2.3 & 2.4 More Gaphs PDF

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TN 2.3 & 2.4 More Graphs for Quantitative Data Stem-and-leaf Plots •

In a stem-and-leaf plot, the data values are split up such that there is a stem and a leaf for each piece of data o For the number 2, zero would be on the stem and 2 would be on the leaf o Example: For the number 25, the number 2 would be on the stem and 5 would be on the leaf o Example: For the number 250, the numbers 2 & 5 would be on the stem and 0 would be on leaf

Example: Ages of dinner guest: 11, 12, 18, 22, 22, 23, 26, 27, 40, 45, 46, 47 Stem-and-Leaf Plot of Dinner Guest Ages

• • • • •

Often, data fall primarily into just a few of the stem rows, we can alter the format slightly and create a split stem and leaf plot In this plot we will divide the stem up into smaller groups and assign each stem two lines on the plot instead of one Leaves with values 0-4 will go on the first line for each stem number Leaves with values 5-9 will go on the second line If a stem line does not have any values of either 0-4 or 5-9 to put on the leaf, that leaf stays blank

Example: Let’s divide each stem group into two groups • •

•

We have two lines with “1” on the stem, two lines with “2”, and the same with “3” and “4” On the first line with a stem of 1, put all leaves 0-4 that go with that stem, and on the second line with a stem of 1, put all the leaves 5-9 that go with that stem Notice, there are no leaves for stems of “3,” so leave them blank (do not put zeroes!)

Split Stem-and-Leaf Plot of Dinner Guest Ages

 A stem and leaf plot gives the same information as a histogram, but it also shows the original •

We can discuss the distribution of the data just as we did with histograms in terms of symmetry and mode

STAT 1107 TN 2.3

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The data reflected in a stem and leaf plot does NOT have to be whole numbers To understand this, let’s go the other direction • •

The stem and leaf plot is given below and you want recreate the data Notice there is information at the bottom of the stem & leaf display that gives you a “key” of sorts for how to interpret the chart

 Recreate the data for this chart using the key below it:

19

1445

20

12

21

0335

22|3 = 22.3 (Could even say 22|3 = 22.39) Stem & Leaf Plot Take-a-ways: • • • • •

The rightmost digit is the leaf, so the leaf consists of only one digit from each data value (the farthest on the right), and the remaining digits form the stem. Stems & leaves are put in numerical order Can be split if best Generally used to display small data Gives same info as a histogram, but shows original data

Dotplots – You will not be asked to make a dot plot on a test or quiz, but the homework problems from the book may include dotplot problems, so you may want to read this section (pg 68) in your book  A dotplot is a graph used to give a rough impression of the shape of a fairly small dataset in which there are repeated numbers Example: The number of siblings for a sample of 20 students 0 5 6 0

STAT 1107 TN 2.3

2 4 0 4

2 15 0 6

2 3 0 4

5 4 3 7

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Time-Series Plots – You will not be asked to create a time-series plot on a test or quiz, but the homework problems from the book may include time-series problems  A time-series plot may be used when data consist of values of a variable measured at different points in time •

Example, the unemployment rate for years 1989-2012 is reported below and represented on a time-series plot

Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Rate 5.3 5.6 6.8 7.5 6.9 6.1 5.6 5.4 4.9 4.5 4.2 4 4.7 5.8 6 5.5 5.1 4.6 4.6 5.8 9.3 9.6 8.9 8.1

Time Series Plot of Unemployment Rate 10

9

Rate

8

7

6

5

4 1 989

1 993

1 997

2001

2005

2009

Year

Graphs can be Misleading • • •

Read this section of the book This is an important section to help you understand how you can be misled by poorly represented statistics In particular, note the area principle and the importance of a good vertical scale

VS The first graph accurately displays the difference, but 3-D graphs can make the bars look shorter than they are

Picture graphs can also give misleading impressions STAT 1107 TN 2.3

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