Displaying Quantitative Displaying Quantitative Data with HistogramsData with Histograms

1.2 cont.1.2 cont.

Hw:Hw: pg 45: 53, 56, 57, 59, 60, 69 pg 45: 53, 56, 57, 59, 60, 69 - 74- 74

Target Goal: I can construct a histogram by Target Goal: I can construct a histogram by hand and with the calculator.hand and with the calculator.

Displaying Displaying Quantitative Quantitative VariablesVariables

HistogramsHistograms The most common graph for The most common graph for distribution of distribution of one quantitative variable.one quantitative variable. No spaces between groups. No spaces between groups.

How to construct a histogramHow to construct a histogram

1. Divide range of data into 1. Divide range of data into classes of equal widthclasses of equal width and count number of observations in each class; and count number of observations in each class; be sure to be sure to specify classes preciselyspecify classes precisely so that each so that each observation falls into exactly one class. observation falls into exactly one class.

2. Label and scale axis and 2. Label and scale axis and title graphtitle graph!!

3. Draw a bar that represents the 3. Draw a bar that represents the countcount in each in each class. class.

Remember:Remember:• Leave Leave no space no space

between bars.between bars.

• Add a break-in-scale Add a break-in-scale symbol (//) on an axis symbol (//) on an axis that does not start at that does not start at 0.0.

• 5 classes 5 classes is a good is a good minimum. minimum.

• Histogram Tips (page Histogram Tips (page 39)39)

Example Drive Time Example Drive Time Professor Moore, who lives a few Professor Moore, who lives a few miles outside a college town, miles outside a college town, records the time he takes to drive records the time he takes to drive to the college each morning. to the college each morning. You You previously entered the times (in previously entered the times (in minutes) into a list name “DRVTM” minutes) into a list name “DRVTM” (pg.46, ex. 55) (pg.46, ex. 55) for the 42 for the 42 consecutive weekdays, with the consecutive weekdays, with the dates in order along the rows. dates in order along the rows.

. . a. a. Fill in freq. column and construct Fill in freq. column and construct

histogram.histogram.

Drivetime FrequencyDrivetime Frequency6.5-7.06.5-7.0 117.0-7.57.0-7.5 227.5 -8.07.5 -8.0 888.0-8.58.0-8.5 11118.5-9.08.5-9.0 12129.0-9.59.0-9.5 669.5-10.09.5-10.0 1110.0-10.510.0-10.5 11

• B. Graph B. Graph (Note: Your graph needs to be specific)(Note: Your graph needs to be specific)

Is the distribution roughly symmetric, Is the distribution roughly symmetric, clearly skewed, or neither? Are there any clearly skewed, or neither? Are there any clear outliers?clear outliers?The distribution is roughly symmetric with no The distribution is roughly symmetric with no clear outliersclear outliers..

Drivetime

.Freq

c. Make a calculator histogram of c. Make a calculator histogram of these drive times.these drive times.

Make calculator histogram and use the trace key.Make calculator histogram and use the trace key.• STATPLOT:STATPLOT:Plot1:OnPlot1:On

– Xlist:2ndSTAT:DRVTM:ENTERXlist:2ndSTAT:DRVTM:ENTER– Freq:1 (sometimes need to press ALPHA 1)Freq:1 (sometimes need to press ALPHA 1)

• WindowWindow– Xmin=6, Xmax=11, Xscl=.5, ymin=0, ymax=13, Xmin=6, Xmax=11, Xscl=.5, ymin=0, ymax=13,

yscl=1,xres=1yscl=1,xres=1

• Use the following classes and determine frequencies.Use the following classes and determine frequencies.

• Can use Technology Toolbox as reference(p.38)Can use Technology Toolbox as reference(p.38)

• Used throughout the book to guide you step by step through Used throughout the book to guide you step by step through various calculator functionalities.various calculator functionalities.

Using Histograms WiselyUsing Histograms Wisely

spaces between bars

no spaces between bars

1. Don’t confuse histograms with bar graphs.•Bar Graph: ____________, compares the distribution of ______________.•Histograms: ______________, the distribution of ______________________.

categorical data

varone quantitaive iable

2.2.Don’t use Don’t use counts (freq) or percents counts (freq) or percents (relative freq) (relative freq) as data.as data.

Length: Length:

1 2 3 4 5 6 7 8 9 10 11 12 131 2 3 4 5 6 7 8 9 10 11 12 13

Count: Count:

1 15 25 7 5 7 8 7 7 6 8 31 15 25 7 5 7 8 7 7 6 8 3 11

Graphed IncorrectlyGraphed Incorrectly Draw Graph Draw Graph CorrectlyCorrectly

3.3. Use percentsUse percents instead of counts on the instead of counts on the vertical axis when comparing distributions vertical axis when comparing distributions with with different numbers of observationsdifferent numbers of observations..

Mary compared the number of letters in the Mary compared the number of letters in the first first 200 200 words of a medical journal and of words of a medical journal and of the first the first 100100 words of an article from an words of an article from an airline magazine. airline magazine.