HistogramsHistograms

Lecture 18Lecture 18Sec. 4.4.4Sec. 4.4.4Tue, Feb 17, 2004Tue, Feb 17, 2004

HistogramsHistograms HistogramHistogram – A display of – A display of

continuous quantitative data in continuous quantitative data in which the data are divided into which the data are divided into classesclasses and rectangles represent and rectangles represent the frequencies of the classes.the frequencies of the classes.

Drawing HistogramsDrawing Histograms Use Data Set 1 on p. 184.Use Data Set 1 on p. 184. Find the maximum value, the Find the maximum value, the

minimum value, and the range.minimum value, and the range. Maximum = 51Maximum = 51 Minimum = 32Minimum = 32 Range = Max – Min = 51 – 32 = 19.Range = Max – Min = 51 – 32 = 19.

Drawing HistogramsDrawing Histograms Divide the data into Divide the data into classesclasses of of

equal width.equal width. The classes must not overlap.The classes must not overlap.

Choose a convenient starting point.Choose a convenient starting point. Choose a convenient class width.Choose a convenient class width. Write the endpoints of each class.Write the endpoints of each class.

Drawing HistogramsDrawing Histograms Starting point = 30.Starting point = 30. Class width = 5.Class width = 5. Classes:Classes:

30 up to 35 (but not including 35).30 up to 35 (but not including 35). 35 up to 40.35 up to 40. 40 up to 45.40 up to 45. 45 up to 50.45 up to 50. 50 up to 55.50 up to 55.

Drawing HistogramsDrawing Histograms We may denote the classes in We may denote the classes in

either of two ways.either of two ways. Interval notation: [low, high)Interval notation: [low, high)

[30, 35), [30, 35), [35, 40),[35, 40), [40, 45), etc.[40, 45), etc. [ and ] mean “include endpoints.”[ and ] mean “include endpoints.” ( and ) mean “exclude endpoints.”( and ) mean “exclude endpoints.”

Drawing HistogramsDrawing Histograms Range notation: low – highRange notation: low – high

30 – 34,30 – 34, 35 – 39,35 – 39, 40 – 44, etc.40 – 44, etc. This notation does not indicate This notation does not indicate

whether the endpoints are included.whether the endpoints are included. Therefore, be sure the endpoints do Therefore, be sure the endpoints do

not overlap.not overlap.

Drawing HistogramsDrawing Histograms Count the number of observations Count the number of observations

in each class. This is the in each class. This is the frequencyfrequency of the class. of the class.

ClassClass FrequencyFrequency[30, 35)[30, 35) 11[35, 40)[35, 40) 22[40, 45)[40, 45) 88[45, 50)[45, 50) 77[50, 55)[50, 55) 22

Drawing HistogramsDrawing Histograms Draw horizontal and vertical axes.Draw horizontal and vertical axes. On the horizontal axis, show the On the horizontal axis, show the

class boundaries.class boundaries. On the vertical axis, show uniform On the vertical axis, show uniform

reference points representing reference points representing frequencies apropos to the data.frequencies apropos to the data. For example, 0, 2, 4, …For example, 0, 2, 4, …

Drawing HistogramsDrawing Histograms

30 35 40 45 50 55Age

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Frequency

Drawing HistogramsDrawing Histograms Over each class, draw a rectangle Over each class, draw a rectangle

whose height is the frequency of whose height is the frequency of that class.that class.

Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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Drawing HistogramsDrawing Histograms

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GuidelinesGuidelines Never use too few or too many classes.Never use too few or too many classes.

Usually 5 to 12 classes is about right.Usually 5 to 12 classes is about right. Use simple round numbers for the Use simple round numbers for the

class boundaries.class boundaries. Mark off the vertical axis uniformly, Mark off the vertical axis uniformly,

showing regular reference points, not showing regular reference points, not the actual frequencies.the actual frequencies.

Frequencies must start at 0.Frequencies must start at 0.

Let’s Do It!Let’s Do It! Let’s do it! 4.14, p. 224 – Let’s do it! 4.14, p. 224 –

Histogram of Household Income.Histogram of Household Income. Let’s do it! 4.16, p. 226 – Let’s do it! 4.16, p. 226 –

Matching Shapes to Matching Shapes to Characteristics.Characteristics.

ExampleExample See Example 4.10, p. 227 – See Example 4.10, p. 227 –

Histogram versus Bar Graph.Histogram versus Bar Graph.

Histograms on the TI-Histograms on the TI-8383 See page 263 for more detailed See page 263 for more detailed

instructions.instructions. Enter the data into list LEnter the data into list L11..

{45, 41, 51, …, 37} {45, 41, 51, …, 37} L L11 Press STAT PLOTPress STAT PLOT

Turn Plot1 On.Turn Plot1 On. Select Histogram Type.Select Histogram Type. Specify List LSpecify List L11..

Histograms on the TI-Histograms on the TI-8383 Press WINDOWPress WINDOW

Set Xmin to the starting point.Set Xmin to the starting point. Set Xmax to the last endpoint.Set Xmax to the last endpoint. Set Xscl to the class width.Set Xscl to the class width. Set Ymin to 0.Set Ymin to 0. Set Ymax to the maximum frequency.Set Ymax to the maximum frequency.

Press GRAPHPress GRAPH The histogram appears.The histogram appears.

Frequency Frequency Distributions on the TI-Distributions on the TI-8383 After getting the histogram, press After getting the histogram, press

TRACE.TRACE. The display shows the first class and The display shows the first class and

its frequency.its frequency. Use the left arrow to see the other Use the left arrow to see the other

class frequencies.class frequencies.

AssignmentAssignment Page 227: Exercises 30 – 38.Page 227: Exercises 30 – 38. Page 249: Exercises 68, 69.Page 249: Exercises 68, 69.