AP Statistics – 1.2 Notes Name: __________________ Displaying Quantitative Data with Graphs

1. Make and Interpret dotplots and stemplots of quantitative data 2. Describe the overall pattern (SOCS) of a distribution and identify any major departures

Here are the number of calories per serving for 16 brands of frozen cheese pizza, along with a dotplot of the data: 340 340 310 320 310 360 350 330 260 380 340 320 360 290 320 330

Describe the Distribution of Calories:

• Shape:

• Center:

• Spread:

• Outliers:

Describing Shape:

Calories260 280 300 320 340 360 380 400

Frozen Pizza Dot Plot

Key

unimodal androughly symmetric with a main clusterbetween 310and360 CaloriesMiddlevalue is 330Calories

Range is from 260to 380Calories

One pizza has an unusually small amount ofcalories 260

Roughly Symmetric Skewedleft skewedRight

uniformunimodal Bimodal

an n

AP Statistics – 1.2 Notes Name: __________________ Displaying Quantitative Data with Graphs

3. Compare distributions of quantitative data using dotplots, stemplots, or histograms How do the numbers of people living in households in the United Kingdom (U.K) and South Africa compare? To help answer the question, we used Census At School’s “Random Data Selector” to choose 50 students from each country. Here are dotplots of the household sizes reported by the survey respondents. Compare the distributions of household sizes for these two countries. South Africa Describe Both Distributions

United Kingdom

Draw Conclusions

Stem-and-leaf plots Ms. Barbero is an AP Statistics teacher and has gathered some interesting information about her students. Below shows a stem-and-leaf plot of her male students and the number of pairs of shoes he owns. Stemplot Split Stems Describing Stemplots

0 4 5 5 5 6 7 7 7 7 8 10 10 10 10 11 12 14 22 35 38

S Unimodalandskewedright0 26 isunusuallylargeandPossibly 15tooe Middle is 6peopleS range is from 3to26people 23S Roughlysymmetricandunimodal0 Nooutlierse midpoint4peopleS range 2 to6people 4

TheSouthAfricandistribution isskewedrightwhilethe vK isroughlysymmetricSouthAfricanhouseholdsizes tend tobelarger with a midpointof 6us 4SouthAfricanhousehold sizesvarymorethanUK witharange of 23vs 4 TheVK householdsareconsistentlysmallerin size SouthAfrican householdshavetwopotentialhighoutliersandtheU.Khouseholdshavenone

o t o skewedRight5 a

small large

AP Statistics – 1.2 Notes Name: __________________ Displaying Quantitative Data with Graphs

4. Identify the shape of a distribution from a graph as roughly symmetric or skewed Independent Practice Using the class data table, collected from the first day of school, create a back-to-back stemplot and compare the heights of males and females from this class.

Female (cm)

Male (cm)

150 152 152 165 158 168 159 170 160 173 163 175 163 178 163 178 165 178 165 180 170 180 173 183

5. Make and interpret histograms of quantitative data

Create a histogram using the males heights in centimeters.

• Divide the data classes (bins) of equal width • Find the frequency (count) of individuals in each class. • Label and scale your axes and draw histogram.

Class Size Matters! • Small Bins may have too many gaps • Large bins may hide gaps

Keyfemale made 153 represents a student153cmtall

20152 s femalesheights are symmetric9 8 15 andmales are skewed left

33 30 1655 16 58 O Males seem to have 1 lowoutlier

3 03 c Typicallymales aretallerwith

17 5 88 818 003 a centerof 176.5 us 163

8 s Males heights vary morewith a range of 31 vs 21

Bins150toa155 I155to460 0160toL165 o

165toL170 2 4

120toL175 2 I 3125toL180 4 aigotoL 1853

150 155 160 165 no 125180 185

Maleheights cm

AP Statistics – 1.2 Notes Name: __________________ Displaying Quantitative Data with Graphs

Practice Problems: a) How do the annual energy costs (in dollars) compare for refrigerators with top freezers and

refrigerators with bottom freezers? The data below are from the May 2010 issue of Consumer Reports.

Compare the distributions of energy cost for these two types of refrigerators.

b) The table presents the average points scored per game (PPG) for the 30 NBA teams in the 2012–2013 regular season. Create a histogram to distribute each teams average PPG.

Team PPG Team PPG Team PPG Atlanta Hawks 98.0 Houston Rockets 106.0 Oklahoma City Thunder 105.7 Boston Celtics 96.5 Indiana Pacers 94.7 Orlando Magic 94.1 Brooklyn Nets 96.9 Los Angeles Clippers 101.1 Philadelphia 76ers 93.2 Charlotte Bobcats 93.4 Los Angeles Lakers 102.2 Phoenix Suns 95.2 Chicago Bulls 93.2 Memphis Grizzlies 93.4 Portland Trail Blazers 97.5 Cleveland Cavaliers 96.5 Miami Heat 102.9 Sacramento Kings 100.2 Dallas Mavericks 101.1 Milwaukee Bucks 98.9 San Antonio Spurs 103.0 Denver Nuggets 106.1 Minnesota Timberwolves 95.7 Toronto Raptors 97.2 Detroit Pistons 94.9 New Orleans Hornets 94.1 Utah Jazz 98.0 Golden State Warriors 101.2 New York Knicks 100.0 Washington Wizards 93.2

EnergyCost

Type

14012611298847056

bottom

top

Dotplot of EnergyCost vs Type

Shape Bottomfreezers looksskewedrightandpossiblybimodal Topfreezers looks roughlysymmetriccenter Bottomfreezerstypicallycostmore withmidpoint of 69vs 56Spread Bottomfreezersvarymuchmore in costoutliers Bottomfreezershave 2unusuallyhighcostsandtopfreezershad

none

no93to 95 995to a97 5 s 8y92to a99 5 g 699to a101 2 fo4 4101toa103 5103toa105 i 2105toclot 3 f g'saidawi isvision

ppg