# Chapter 4 Displaying Quantitative Data

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16-Jan-2016Category

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### Transcript of Chapter 4 Displaying Quantitative Data

Chapter 4

Displaying Quantitative Data

Graphs for Quantitative Data

DotplotUsed with numerical data (either discrete or continuous)Made by putting dots (or Xs) on a number lineCan make comparative dotplots by using the same axis for multiple groups. Be sure to label the boxplots.Used for small sets of data.

Distribution Activity . . .

Types (Shapes)of Distributions

Symmetricalrefers to data in which both sides are (more or less) the same when the graph is folded vertically down the middlebell-shaped is a special typehas a center mound with two sloping tails

Uniformrefers to data in which every class has equal or approximately equal frequency

Skewed (left/negatively or right/positively)refers to data in which one side (tail) is longer than the other sidethe direction of skewness is on the side of the longer tail

Bimodal (multi-modal)refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

How to describe a numerical, univariate graph

What strikes you as the most distinctive difference among the distributions of exam scores in classes A, B, & C ?

1. Centerdiscuss where the middle of the data fallsthree types of central tendencymean, median, & mode

What strikes you as the most distinctive difference among the distributions of scores in classes D, E, & F?

2. Spreaddiscuss how spread out the data isrefers to the variability of the dataRange, standard deviation, IQR

What strikes you as the most distinctive difference among the distributions of exam scores in classes G, H, & I ?

3. Shaperefers to the overall shape of the distributionsymmetrical, uniform, skewed, or bimodal

What strikes you as the most distinctive difference among the distribution of exam scores in class J ?

What strikes you as the most distinctive difference among the distribution of exam scores in class K ?

4. Unusual occurrencesoutliers - value that lies away from the rest of the datagapsclustersanything else unusual

What strikes you as the most distinctive difference among the distribution of exam scores in class L ?

5. In contextYou must write your answer in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!

More Graphs for Quantitative Data

Stemplots (Stem & Leaf Plots)Used with univariate, numerical dataMust have key so that we know how to read numbersCan split stems when you have long list of leavesCan have a comparative stemplot with two groups

Would a stemplot be a good graph for the number of pieces of gun chewed per day by AP Stat students? Why or why not?Would a stemplot be a good graph for the number of pairs of shoes owned by AP Stat students? Why or why not?

Example:The following data are price per ounce for various brands of dandruff shampoo at a local grocery store.0.320.210.290.540.170.280.360.23

Can you make a stemplot with this data?

Example: Tobacco use in G-rated Movies

Total tobacco exposure time (in seconds) for Disney movies:223176548371585129937 111657492623206 9

Total tobacco exposure time (in seconds) for other studios movies:20516261117591155 245517

Make a comparative (back-to-back) stemplot.

HistogramsUsed with numerical dataBars touch on histogramsTwo typesDiscreteBars are centered over discrete valuesContinuousBars cover a class (interval) of valuesFor comparative histograms use two separate graphs with the same scale on the horizontal axisWould a histogram be a good graph for the fastest speed driven by AP Stat students? Why or why not?Would a histogram be a good graph for the number of pieces of gum chewed per day by AP Stat students? Why or why not?

The two histograms below display the distribution of heights of gymnasts and the distribution of heights of female basketball players. Which is which? Why?Heights Figure AHeights Figure B

Suppose you found a pair of size 6 shoes left outside the locker room. Which team would you go to first to find the owner of the shoes? Why?

Suppose a tall woman (5 ft 11 in) tells you see is looking for her sister who is practicing with a gym. To which team would you send her? Why?What aspects of the graphs helped you answer these questions?

Electronic Components ExampleManufacturing an electronic component requires attaching very fine wires to a semiconductor wafer. If the strength of the bond is weak, the component may fail. Here are the measurements of the breaking strength (in pounds) of 23 connections.0055075095095011501150115011501150125012501350145014501450155015501550185020503150

ScatterplotShows the relationship between two quantitative variables measured on the same individualThe values of one individual appear on the horizontal axis, and the values of the other variable appear on the vertical axis.

TimeplotsDisplay data that change over timeSuccessive values are usually connected with lines to show trends more clearly.

Cumulative Relative Frequency Plot(Ogive). . . is used to answer questions about percentiles. Percentiles are the percent of individuals that are at or below a certain value.Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2?Interquartile Range (IQR) is the range of the middle half (50%) of the data.IQR = Q3 Q1

*Do after Features of Distributions Activity*Center & spread