MAED 3103 - 002 SPRING 1996

Introduction to Data Analysis
Using the TI-82 Calculator
Section 2

Organizing Data - Line Plots

We will look at some apple data taken from Investigating Apples, Christine V. Johnson, Addison Wesley. Since she comes from the state of Washington, she has quite a bit of data at hand.

After being harvested apples are sorted by size and packed in fiberboard boxes for shipment. Each box contains 42 pounds of fruit, packed by count. For example, a size 100 box has 100 apples of equal size for a combined weight of 42 pounds. Other standard sizes range from 48 to 216. Sizes 48 through 80 are considered large apples, 88 through 125 are medium apples, and 138 through 214 are small apples. The following table gives approximate masses of different sizes of apples.

Scale of Size and Approximate Mass
Apples

Size	Mass in Grams	Size	Mass in Grams
48	397	125	153
56	340	138	136
64	298	150	127
72	264	163	116
80	238	175	108
88	215	198	96
100	190	216	88
113	167

We are given the following data about 36 size-80 apples of three different varieties.

Red Delicious	Red Delicious	Granny Smith	Granny Smith	Rome Beauty	Rome Beauty
204	238	227	220	187	203
212	239	193	221	188	205
215	239	214	223	188	206
221	239	206	217	192	206
221	240	224	206	192	207
222	241	237	228	192	207
223	241	209	205	193	210
224	241	210	229	194	210
225	242	228	229	196	217
226	245	231	229	198	217
226	247	214	230	198	219
227	248	186	211	199	220
231	253	215	235	200	224
231	255	216	206	200	228
233	257	212	239	200	228
233	263	217	240	200	231
234	264	219	241	201	236
237	266	220	245	202	246

We will construct line plots for this data. Line plots are quick and simple ways to organize data. From a line plot it is easy to spot the largest and smallest values, outliers, clusters, and gaps in the data. It gives a nice presentation of the distribution and shows us a technique for computing the median value. The line plots for these data sets are constructed as follows:

Draw a horizontal line and put a scale of numbers on the line that runs from the least to the largest values of the data. In our examples above our scale will run from 190 to 266 for the Red Delicious apples and 180 to 256 for the other two varieties. Then put an X at the appropriate value for each data value in your list.

You construct the line plots for the other two sets of data.

Some of the features that we see from a line plot that are not apparent in a list of numbers are:

• Outliers - data values that are substantially larger or smaller than the other values.

• Clusters - isolated groups of points

• Gaps - large spaces between data points.

It is easy to spot the largest and smallest values from your line plot. This is not true of a list of numbers unless they are ordered.

Section 3: Organizing Data - Stem and Leaf Plots

MAED 3103 - Technology and Mathematics Education Spring 1996

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