Lesson 3 Exploring Data with Graphs and Numerical Summaries

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Lesson 3 Exploring Data with Graphs and Numerical Summaries Learn …. The Use of Graphs to Describe Quantitative Data Numerical Measures for Central Tendency Graphs for Quantitative Data Dot Plot: shows a dot for each observation

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Lesson 3Exploring Data with Graphs and Numerical Summaries
• Learn ….

The Use of Graphs to Describe

Quantitative Data

Numerical Measures for Central Tendency

Graphs for Quantitative Data
• Dot Plot: shows a dot for each observation
• Stem-and-Leaf Plot: portrays the individual observations
• Histogram: uses bars to portray the data
Dotplot for Sodium in Cereals
• Sodium Data:

0 210 260 125 220 290 210 140 220 200 125 170 250 150 170 70 230 200 290 180

Stem-and-Leaf Plot for Sodium in Cereal

Sodium Data: 0 210

260 125

220 290

210 140

220 200

125 170

250 150

170 70

230 200

290 180

Frequency Table

Sodium Data:

0 210

260 125

220 290

210 140

220 200

125 170

250 150

170 70

230 200

290 180

Which Graph?
• Dot-plot and stem-and-leaf plot:
• More useful for small data sets
• Data values are retained
• Histogram
• More useful for large data sets
• Most compact display
• More flexibility in defining intervals
Shape of a Distribution
• Overall pattern
• Clusters?
• Outliers?
• Symmetric?
• Skewed?
• Unimodal?
• Bimodal?

What shape would you expect a histogram of this data set to have?

• Symmetric
• Skewed to the left
• Skewed to the right
• Bimodal
Consider a data set of the scores of students on a very easy exam in which most score very well but a few score very poorly:

What shape would you expect a histogram of this data set to have?

• Symmetric
• Skewed to the left
• Skewed to the right
• Bimodal
Section 2.3

How Can We describe the Center of Quantitative Data?

Mean
• The sum of the observations divided by the number of observations
Median
• The midpoint of the observations when they are ordered from the smallest to the largest (or from the largest to the smallest)
Find the mean and median

CO2 Pollution levels in 8 largest nations measured in metric tons per person:

2.3 1.1 19.7 9.8 1.8 1.2 0.7 0.2

• Mean = 4.6 Median = 1.5
• Mean = 4.6 Median = 5.8
• Mean = 1.5 Median = 4.6
Outlier
• An observation that falls well above or below the overall set of data
• The mean can be highly influenced by an outlier
• The median is resistant: not affected by an outlier
Mode
• The value that occurs most frequently.
• The mode is most often used with categorical data