Organizing Quantitative DataSection 2.2

Alan Craig770-274-5242

acraig@gpc.edu

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Objectives 2.2

1. Summarize discrete data in tables.

2. Construct histograms of discrete data.

3. Summarize continuous data in tables.

4. Construct histograms of continuous data.

5. Draw stem-and-leaf plots.

6. Identify the shape of a distribution.

7. Draw time series graphs.

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Construct Table #6, p66

Number Free RelativeThrows Frequency Frequency1 16 .322 11 .223 9 .184 7 .14 (b)5 2 .046 3 .067 0 .00 (d)8 1 .029 0 .0010 1 .02 (c)

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Definition

Histogram

• A histogram is constructed by drawing rectangles for each class of data.

• The height of each rectangle is the frequency or relative frequency of the class.

• The width of each rectangle should be the same and the rectangles should touch each other.

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Histogram for #6, p66Histogram of Number of Free Throws

Until a Miss

0

2

4

6

8

10

12

14

16

18

1 3 5 7 9M

ore

Free Throws Until a Miss

Fre

qu

ency

Frequency

Note: Histogram created using Excel Data Analysis (see p. 71)

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Using TI-84+ for a Histogram

1. Enter number free throws in L1 and Frequency in L2 using STAT1:Edit

2. 2nd Y=1:Plot1 On Enter3. Select histogram icon Enter4. Xlist L1 5. Freq 2nd 2 to select L26. WINDOW Set Xmin, Xmax, Xscl

(Note: Using ZOOM9:ZoomStat lets the calculator set these values and automatically graphs the histogram.)

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Using TI-84+ for a Histogram

7. For discrete data, set Xmin to lowest x value - ½ width of your bars and Xmax to the largest x value + ½ width. Set Xscl to the width of each bar.

8. For our data, set Xscl to 1, Xmin to 0.5, and Xmax to 10.5

9. GRAPH

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“Free Throw” Histogram from TI-84+

Note that the calculator does not label information on the graph. Use TRACE to find classes and frequencies.

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Tables & Histograms for Continuous Data

• Create classes—categories of data using intervals

• Lower class limit—smallest value in a class• Upper class limit—largest value in a class• Class width—difference between consecutive

lower class limits• Open ended—if the last class does not have an

upper class limit

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Tables & Histograms for Continuous Data

• Example—see Tables 12 & 13, pp. 57-58.

• Arbitrarily set lower class limit to 10 and class width to 5

• Classes must not overlap, so 10 – 14.9, 15 – 19.9,…

• For Histogram in Figure 9 (a), enter midpoints of each class in Table 13 in L1 and the corresponding frequency in L2

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Tables & Histograms for Continuous Data

• In STATPLOT, ensure Plot1 is ON, histogram is selected, Xlist = L1 and Freq = L2

• In WINDOW, set Xmin = 10, Xmax = 50, Xscl = 5, Ymin = -1, Ymax =12

• Now GRAPH

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Constructing Stem & Leaf Plots

Step 1: Stem consists of the digits to the left of the rightmost digit. The leaf will be the rightmost digit.

Step 2: Write the stems in a vertical column in increasing order. Draw a vertical line to the right of the stems.

Step 3: Write each leaf corresponding to the stems to the right of the vertical line. Leaves must be written in ascending order.

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Example Stem & Leaf#26, p69

0 5 6 7

1 2 2 2 3 3 5 5 7 8 8 8 9

2 1 4 5 6 6 8

3 4 5 8 9 9

4 0 1 1 3 3 5 6 9

5 2 3 5 6 6

6 1 3 3 4 5 8

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Distribution Shapes

• Symmetric—right & left sides are mirror images– Uniform—each class has same frequency– Bell-shaped—highest in middle, equal tails

• Skewed Left—longer tail to left

• Skewed Right—longer tail to right

• See the histograms, top of p. 63

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Definition

Time Series Plot

• Plot time on the horizontal axis (x-axis) and the corresponding value of the variable on the vertical axis (y-axis). Lines are then drawn connecting the points.

• Time series plots are very useful in identifying trends in the data.

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Time Series PlotWalmart Earnings Per Share

$1.47

$1.79

$2.07

$2.41

$2.68

$-

$0.50

$1.00

$1.50

$2.00

$2.50

$3.00

2002 2003 2004 2005 2006

Fiscal Year

EP

S

Earnings Per Share

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Questions

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